# Publications since 2010

## 2018

**Giesselmann, J.; Kolbe, N.; Lukacova-Medvidova, M. & Sfakianakis, N.:**Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model,

*Accepted for publication in Discrete Contin. Dyn. Syst. Ser. B.,*

**2018**.

**Gimperlein, H.; Meyer, F.; Özdemir, C.; Stark, D. & Stephan, E. P.:**Boundary elements with mesh refinements for the wave equation.,

*Numer. Math.,*

**2018**, (accepted).

**Gimperlein, H.; Meyer, F.; Özdemir, C. & Stephan, E. P.:**Time domain boundary elements for dynamic contact problems,

*Computer Methods in Applied Mechanics and Engineering,*

**2018**

*, 333*, 147 - 175.

**Köppel, M.; Martin, V.; Jaffré, J. & Roberts, J. E.:**A Lagrange multiplier method for a discrete fracture model for flow in porous media,

*(submitted),*

**2018**.

**Köppel, M.; Martin, V. & Roberts, J. E.:**A stabilized Lagrange multiplier finite-element method for flow in porous media with fractures,

*(submitted),*

**2018**.

**Raja Sekhar, G. P.; Sharanya, V. & Rohde, C.:**Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number,

*erscheint bei Int. J. Multiph. Flow,*

**2018**.

**Rohde, C. & Zeiler, C.:**On Riemann Solvers and Kinetic Relations for Isothermal Two-Phase Flows with Surface Tension,

*erscheint bei Z. Angew. Math. Phys.,*

**2018**.

**Seus, D.; Mitra, K.; Pop, I. S.; Radu, F. A. & Rohde, C.:**A linear domain decomposition method for partially saturated flow in porous media ,

*Comp. Methods in Appl. Mech. Eng,*

**2018**

*, 333*, 331-355.

## 2017

**Armiti-Juber, A. & Rohde, C.:**On Darcy-and Brinkman-Type Models for Two-Phase Flow in Asymptotically Flat Domains,

**2017**.

**Chalons, C.; Magiera, J.; Rohde, C. & Wiebe, M.:**A Finite-Volume Tracking Scheme for Two-Phase Compressible Flow,

*erscheint bei Springer Proc. Math. Stat.,*

**2017**.

**Chalons, C.; Rohde, C. & Wiebe, M.:**A Finite Volume Method for Undercompressive Shock Waves in Two Space Dimensions,

*ESAIM Math. Model. Numer. Anal.,*

**2017**

*, 51*, 1987-2015.

**Fechter, S.; Munz, C.-D.; Rohde, C. & Zeiler, C.:**A sharp interface method for compressible liquid-vapor flow with phase transition and surface tension,

*J. Comput. Phys.,*

**2017**

*, 336*, 347-374.

**Fechter, S.; Munz, C.-D.; Rohde, C. & Zeiler, C.:**Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension,

*Comput. & Fluids,*

**2017**.

**Feistauer, M.; Bartos, O.; Roskovec, F. & Sändig, A.-M.:**Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition,

*Proceeding of the EQUADIFF 17,*

**2017**, 127-136.

**Feistauer, M.; Roskovec, F. & Sändig, A.-M.:**Discontinuous Galerkin Method for an Elliptic Problem with Nonlinear Boundary Conditions in a Polygon,

*IMA,*

**2017**

*, 00*, 1-31.

**Giesselmann, J.; Lattanzio, C. & Tzavaras, A. E.:**Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics,

*Arch. Ration. Mech. Anal.,*

**2017**

*, 223*, 1427 - 1484.

**Giesselmann, J. & Pryer, T.:**A posteriori analysis for dynamic model adaptation in convection dominated problems,

*Math. Models Methods Appl. Sci. (M3AS),*

**2017**

*, 27*, 2381 - 2423.

**Giesselmann, J. & Pryer, T.:**

*Clement Cances and Pascal Omnes*

*(Eds.)*, Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model,

*Finite Volumes for Complex Applications VIII-Methods and Theoretical Aspects,*

**2017**

*, 199*.

**Giesselmann, J. & Tzavaras, A. E.:**Stability properties of the Euler-Korteweg system with nonmonotone pressures,

*Appl. Anal.,*

**2017**

*, 96*, 1528-1546.

**Gutt, R.; Kohr, M.; Mikhailov, S. & Wendland, W. L.:**On the mixed problem for the semilinear Darcy-Forchheimer-Brinkman systems in Besov spaces on creased Lipschitz domains,

*Math. Meth. Appl. Sci.,*

**2017**

*, 18*, 7780-7829.

**Harbrecht, H.; Wendland, W. L. & Zorii, N.:**Riesz energy problems for strongly singular kernels,

*Math. Nachr.,*

**2017**.

**Kohr, M.; Medkova, D. & Wendland, W. L.:**On the Oseen-Brinkman flow around an (m-1)-dimensional obstacle,

*Monatshefte für Mathematik,*

**2017**

*, 483*, 269-302.

**Kohr, M.; Mikhailov, S. & Wendland, W. L.:**Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian mani,

*J of Mathematical Fluid Mechanics,*

**2017**

*, 19*, 203-238.

**Köppel, M.; Kröker, I. & Rohde, C.:**Intrusive Uncertainty Quantification for Hyperbolic-Elliptic Systems Governing Two-Phase Flow in Heterogeneous Porous Media,

*Comput. Geosci.,*

**2017**

*, 21*, 807-832.

**Kutter, M.; Rohde, C. & Sändig, A.-M.:**Well-Posedness of a Two Scale Model for Liquid Phase Epitaxy with Elasticity,

*Contin. Mech. Thermodyn.,*

**2017**

*, 29*, 989-1016.

**Magiera, J. & Rohde, C.:**A Particle-based Multiscale Solver for Compressible Liquid-Vapor Flow,

*erscheint bei Springer Proc. Math. Stat.,*

**2017**.

**Rohde, C.:**Fully Resolved Compressible Two-Phase Flow: Modelling, Analytical and Numerical Issues,

**2017**.

**Seus, D.; Radu, F. A. & Rohde, C.:**A linear domain decomposition method for two-phase flow in porous media,

**2017**.

*Maz'ya, V. and Natroshvili, D. and Shargorodsky, E. and Wendland, W. L.*

*(Eds.)*, Recent Trends in Operator Theory and Partial Differential Equations. The Roland Duduchava Anniverary Volume,

*Birkhäuser/Springer International,*

**2017**.

## 2016

**Barth, A.; Bürger, R.; Kröker, I. & Rohde, C.:**Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach,

*Computers & Chemical Engineering ,*

**2016**

*, 89*, 11 - 26.

**Betancourt, F. & Rohde, C.:**Finite-Volume Schemes for Friedrichs Systems with Involutions,

*App. Math. Comput.,*

**2016**

*, 272, Part 2*, 420-439.

**Chertock, A.; Degond, P. & Neusser, J.:**An Asymptotic-Preserving Method for a Relaxation of the Navier-Stokes-Korteweg Equations,

*Journal of Computational Physics,*

**2016**

*, 335*, 387-403.

**Colombo, R. M.; Guerra, G. & Schleper, V.:**The compressible to incompressible limit of 1D Euler equations: the non-smooth case,

*Archive for Rational Mechanics and Analysis,*

**2016**

*, 219*, 701-718.

**Colombo, R. M.; LeFloch, P. G. & Rohde, C.:**Hyperbolic techniques in Modelling, Analysis and Numerics,

*Oberwolfach Reports,*

**2016**

*, 13*, 1683-1751.

**Dedner, A. & Giesselmann, J.:**A posteriori analysis of fully discrete method of lines DG schemes for systems of conservation laws,

*SIAM J. Numer. Anal.,*

**2016**

*, 54*, 3523-3549.

**Diehl, D.; Kremser, J.; Kröner, D. & Rohde, C.:**Numerical Solution of Navier-Stokes-Korteweg Systems by Local Discontinuous Galerkin Methods in Multiple Space Dimensions,

*Appl. Math. Comput.,*

**2016**

*, 272, Part 2*, 309-335.

**Dragomirescu, I.; Eisenschmidt, K.; Rohde, C. & Weigand, B.:**Perturbation solutions for the finite radially symmetric Stefan problem,

*Inter. J. Thermal Sci.,*

**2016**

*, 104*, 386-395.

**Dumbser, M.; Gassner, G.; Rohde, C. & Roller, S.:**Preface to the special issue ``Recent Advances in Numerical Methods for Hyperbolic Partial Differential Equations'',

*Appl. Math. Comput.,*

**2016**

*, 272*, 235-236.

**Giesselmann, J.:**Relative entropy based error estimates for discontinuous Galerkin schemes,

*Bull. Braz. Math. Soc. (N.S.),*

**2016**

*, 47*, 359-372.

**Giesselmann, J. & Pryer, T.:**Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics,

*BIT Numerical Mathematics,*

**2016**

*, 56*, 99 - 127.

**Giesselmann, J. & Pryer, T.:**Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics,

*IMA J. Numer. Anal.,*

**2016**

*, 36*, 1685 - 1714.

**Guerra, G. & Schleper, V.:**A coupling between a 1D compressible-incompressible limit and the 1D p-system in the non smooth case,

*Bulletin of the Brazilian Mathematical Society, New Series,*

**2016**

*, 47*, 381-396.

**Gutt, R.; Kohr, M.; Pintea, C. & Wendland, W. L.:**On the transmission problems for the Oseen and Brinkman systems on Lipschitz domains in compact Riemannian manifolds,

*Math. Nachr,*

**2016**

*, 289*, 471-484.

**Harbrecht, H.; Wendland, W. L. & Zorii, N.:**Rapid solution of minimal Riesz energy problems,

*Numer. Methods Partial Diff. Equ.,*

**2016**

*, 32*, 1535-1552.

**Köppel, M. & Rohde, C.:**Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous Media,

*PAMM Proc. Appl. Math. Mech.,*

*WILEY-VCH Verlag,*

**2016**

*, 16*, 749–750.

**Kabil, B. & Rodrigues, M.:**Spectral validation of the Whitham equations for periodic waves of lattice dynamical systems,

*Journal of Differential Equations,*

**2016**

*, 260*, 2994-3028.

**Kabil, B. & Rohde, C.:**Persistence of undercompressive phase boundaries for isothermal Euler equations including configurational forces and surface tension,

*Math. Meth. Appl. Sci.,*

**2016**

*, 39*, 5409-5426.

**Kohr, M.; de Cristoforis, L.; Mikhailov, S. & Wendland, W. L.:**Integral potential method for transmission problem with Lipschitz interface in R³ for the Stokes and Darcy-Forchheimer-Brinkman PED systems,

*ZAMP,*

**2016**

*, 67:116*, 1-30.

**Kohr, M.; Lanza de Cristoforis, M. & Wendland, W. L.:**On the Robin transmission boundary value problem for the nonlinear Darcy-Forchheimer-Brinkman and Navier-Stokes system,

*J. Math. Fluid Mechanics,*

**2016**

*, 18*, 293-329.

**Kohr, M.; Mikhailov, S. & Wendland, W. L.:**Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds,

*Journal of Mathematical Fluid Dynamics,*

**2016**

*, DOI 10.1007/s 00021-16-0273-6*.

**Kohr, M.; Pintea, C. & Wendland, W. L.:**Poisson transmission problems for L^infty perturbations of the Stokes system on Lipschitz domains on compact Riemannian manifolds,

*J. Dyn. Diff. Equations,*

**2016**

*, DOI 110.1007/s10884-014-9359-0*.

**Magiera, J.; Rohde, C. & Rybak, I.:**A hyperbolic-elliptic model problem for coupled surface-subsurface flow,

*Transp. Porous Media,*

**2016**

*, 114*, 425-455.

**Ostrowski, L.; Ziegler, B. & Rauhut, G.:**Tensor decomposition in potential energy surface representations,

*The Journal of Chemical Physics,*

**2016**

*, 145*, 104103.

**Redeker, M.; Pop, I. S. & Rohde, C.:**Upscaling of a Tri-Phase Phase-Field Model for Precipitation in Porous Media,

*IMA J. Appl. Math.,*

**2016**

*, 81(5)*, 898-939.

**Rossi, E. & Schleper, V.:**Convergence of a numerical scheme for a mixed hyperbolic-parabolic system in two space dimensions,

*ESAIM Math. Model. Numer. An.,*

**2016**

*, 50*, 475-497.

**Rybak, I. & Magiera, J.:**

*T. Dickopf et al.*

*(Eds.)*, Decoupled schemes for free flow and porous medium systems,

*Domain Decomposition Methods in Science and Engineering XXII,*

*Springer,*

**2016**

*, 104*, 613-621.

**Schleper, V.:**A HLL-type Riemann solver for two-phase flow with surface forces and phase transitions,

*Appl. Numer. Math.,*

**2016**

*, 108*, 256-270.

**Sharanya, V.; Raja Sekhar, G. P. & Rohde, C.:**Bed of polydisperse viscous spherical drops under thermocapillary effects,

*Z. Angew. Math. Phys.,*

**2016**

*, 67*, 101.

## 2015

**Giesselmann, J.:**Low Mach asymptotic preserving scheme for the Euler-Korteweg model,

*IMA J. Numer. Anal.,*

**2015**

*, 35*, 802-832.

**Giesselmann, J.:**Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local model,

*J. Differential Equations,*

**2015**

*, 258*, 3589-3606.

**Giesselmann, J.; Makridakis, C. & Pryer, T.:**A posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws,

*SIAM J. Numer. Anal.,*

**2015**

*, 53*, 1280-1303.

**Giesselmann, J. & Pryer, T.:**Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model,

*M2AN Math. Model. Numer. Anal.,*

**2015**

*, 49(1)*, 275-301.

**Grosan, T.; Kohr, M. & Wendland, W. L.:**Dirichlet problem for a nonlinear generalized Darcy-Forchheimer-Brinkman system in Lipschitz domains,

*Math. Meth. Appl. Sciences,*

**2015**

*, 38*, 3615-3628.

**Kissling, F. & Rohde, C.:**The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case,

*Multiscale Model. Simul.,*

**2015**

*, 13 no. 4*, 1507-1541.

**Kohr, M.; Lanza de Cristoforis, M. & Wendland, W. L.:**Poisson problems for semilinear Brinkman systems on Lipschitz domains in R^3,

*ZAMP,*

**2015**

*, 66*, 833-846.

**Kröker, I.; Nowak, W. & Rohde, C.:**A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems,

*Comput. Geosci.,*

*Springer International Publishing,*

**2015**

*, 19*, 269-284.

**Micula, S. & Wendland, W. L.:**Trigonometric collocation for nonlinear Riemann-Hilbert problems in doubly connected domains,

*IMA J. Num. Analysis,*

**2015**

*, 35*, 834-858.

**Neusser, J.; Rohde, C. & Schleper, V.:**Relaxed Navier-Stokes-Korteweg Equations for compressible two-phase flow with phase transition,

*J. Numer. Meth. Fluids,*

**2015**

*, 79*, 615-639.

**Neusser, J.; Rohde, C. & Schleper, V.:**Relaxation of the Navier-Stokes-Korteweg Equations for Compressible Two-Phase Flow with Phase Transition,

*J. Numer. Methods Fluids,*

**2015**

*, 79*, 615-639.

**Rohde, C. & Zeiler, C.:**A relaxation Riemann solver for compressible two-phase flow with phase transition and surface tension,

*Appl. Numer. Math.,*

**2015**

*, 95*, 267-279.

**Rybak, I.; Gray, W. & Miller, C.:**Modeling two-fluid-phase flow and species transport in porous media,

*J. Hydrology,*

**2015**

*, 521*, 565-581.

**Rybak, I.; Magiera, J.; Helmig, R. & Rohde, C.:**Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems,

*Comput. Geosci.,*

**2015**

*, 19*, 299-309.

**Schleper, V.:**A hybrid model for traffic flow and crowd dynamics with random individual properties,

*Math. Biosci. Eng.,*

**2015**

*, 12*, 393-413.

**Schmidt, A.; Dihlmann, M. & Haasdonk, B.:**Basis generation approaches for a reduced basis linear quadratic regulator,

*Proc. MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling,*

**2015**, 713-718.

## 2014

**Aki, G. L.; Dreyer, W.; Giesselmann, J. & Kraus, C.:**A quasi-incompressible diffuse interface model with phase transition,

*Math. Models Methods Appl. Sci.,*

**2014**

*, 24*, 827-861.

**Armiti-Juber, A. & Rohde, C.:**

*Fuhrmann, Jürgen and Ohlberger, Mario and Rohde, Christian*

*(Eds.)*, Almost Parallel Flows in Porous Media,

*Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems,*

*Springer International Publishing,*

**2014**

*, 78*, 873-881.

**Bürger, R.; Kröker, I. & Rohde, C.:**A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit,

*ZAMM Z. Angew. Math. Mech.,*

**2014**

*, 94*, 793-817.

**Chalons, C.; Engel, P. & Rohde, C.:**A Conservative and Convergent Scheme for Undercompressive Shock Waves,

*SIAM J. Numer. Anal.,*

**2014**

*, 52*, 554-579.

**Corli, A.; Rohde, C. & Schleper, V.:**Parabolic approximations of diffusive-dispersive equations.,

*J. Math. Anal. Appl.,*

**2014**

*, 414*, 773-798.

**Dreyer, W.; Giesselmann, J. & Kraus, C.:**A compressible mixture model with phase transition,

*Physica D,*

**2014**

*, 273-274*, 1-13.

**Ehlers, W.; Helmig, R. & Rohde, C.:**Editorial: Deformation and transport phenomena in porous media,

*ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik,*

*WILEY-VCH Verlag,*

**2014**

*, 94*, 559-559.

**Engel, P.; Viorel, A. & Rohde, C.:**A Low-Order Approximation for Viscous-Capillary Phase Transition Dynamics,

*Port. Math.,*

**2014**

*, 70*, 319-344.

**Eymard, R. & Schleper, V.:**Study of a numerical scheme for miscible two-phase flow in porous media,

*Numer. Meth. Part. D. E.,*

**2014**

*, 30*, 723-748.

**Fechter, S.; Zeiler, C.; Munz, C.-D. & Rohde, C.:**Simulation of compressible multi-phase flows at extreme ambient conditions using a Discontinuous-Galerkin Method,

*ILASS–Europe, 26th European Conference on Liquid Atomization and Spray Systems,*

**2014**.

**Giesselmann, J.:**A Relative Entropy Approach to Convergence of a Low Order Approximation to a Nonlinear Elasticity Model with Viscosity and Capillarity,

*SIAM J. Math. Anal.,*

**2014**

*, 46*, 3518-3539.

**Giesselmann, J.; Makridakis, C. & Pryer, T.:**Energy consistent DG methods for the Navier-Stokes-Korteweg system,

*Math. Comp.,*

**2014**

*, 83*, 2071 - 2099.

**Giesselmann, J. & Müller, T.:**Geometric error of finite volume schemes for conservation laws on evolving surfaces,

*Numer. Math.,*

**2014**

*, 128*, 489–516.

**Giesselmann, J. & Müller, T.:**

*J. Fuhrmann, M. Ohlberger and C. Rohde*

*(Eds.)*, Estimating the Geometric Error of Finite Volume Schemes for Conservation Laws on Surfaces for generic numerical flux functions,

*Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects,*

**2014**

*, 77*.

**Giesselmann, J. & Pryer, T.:**

*J. Fuhrmann, M. Ohlberger and C. Rohde*

*(Eds.)*, On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws,

*Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects,*

**2014**

*, 77*.

**Giesselmann, J. & Tzavaras, A. E.:**Singular Limiting Induced from Continuum Solutions and the Problem of Dynamic Cavitation,

*Arch. Ration. Mech. Anal.,*

**2014**

*, 212*, 241-281.

**Giesselmann, J. & Tzavaras, A. E.:**

*F. Ancona, A. Bressan, P. Marcati, A. Marson (Eds.)*

*(Eds.)*, On cavitation in elastodynamics,

*Hyperbolic Problems: Theory, Numerics, Applications,*

*AIMS,*

**2014**, 599-606.

**Harbrecht, H.; Wendland, W. L. & Zorii, N.:**Riesz minimal energy problems on C^k-1,1 manifolds,

*Math. Nachr.,*

**2014**

*, 287*, 48-69.

**Köppel, M.; Kröker, I. & Rohde, C.:**

*Fuhrmann, Jürgen and Ohlberger, Mario and Rohde, Christian*

*(Eds.)*, Stochastic Modeling for Heterogeneous Two-Phase Flow,

*Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects,*

*Springer International Publishing,*

**2014**

*, 77*, 353-361.

**Kabil, B. & Rohde, C.:**The influence of surface tension and configurational forces on the stability of liquid-vapor interfaces,

*Nonlinear Analysis: Theory, Methods & Applications,*

**2014**

*, 107*, 63 - 75.

**Kaulmann, S.; Flemisch, B.; Haasdonk, B.; Lie, K.-A. & Ohlberger, M.:**The Localized Reduced Basis Multiscale method for two-phase flows in porous media,

*arXiv.org,*

**2014**.

**Kohls, K.; Rösch, A. & Siebert, K. G.:**A Posteriori Error Analysis of Optimal Control Problems with Control Constraints,

*SIAM J. Control Optim.,*

**2014**

*, 52(3)*, 1832–1861. (30 pages).

**Kohr, M.; Lanza de Cristoforis, M. & Wendland, W. L.:**Boundary value problems of Robin type for the Brinkman and Darcy-Forchheimer-Brinkman systems in Lipschitz domains,

*J. Math. Fluid Mechanics,*

**2014**

*, 16*, 595 - 830.

**Kohr, M.; Lanza de Cristoforis, M. & Wendland, W. L.:**

*T. Aliev Azerogly, A. Goldberg and S.V. Rogosin*

*(Eds.)*, Nonlinear Darcy-Forchheimer-Brinkman system with linear boundary conditions in Lipschitz domains,

*Complex Analysis and Potential Theory with Applications,*

*Cambridge Sci. Publ.,*

**2014**, 111-124.

**Kohr, M.; Pintea, C. & Wendland, W. L.:**Neumann-transmission problems for pseudodifferential Brinkman operators on Lipschitz domains in compact Riemannian manifolds,

*Communications in Pure and Applied Analysis,*

**2014**

*, 13*, 1-28.

**Maier, I. & Haasdonk, B.:**A Dirichlet-Neumann reduced basis method for homogeneous domain decomposition problems,

*Applied Numerical Mathematics,*

**2014**

*, 78*, 31-48.

**Rossi, E. & Schleper, V.:**Convergence of a numerical scheme for a mixed hyperbolic-parabolic system in two space dimensions,

**2014**.

**Rybak, I.:**

*Fuhrmann, J. and Ohlberger, M. and Rohde, C.*

*(Eds.)*, Coupling free flow and porous medium flow systems using sharp interface and transition region concepts,

*Finite Volumes for Complex Applications VII - Elliptic, Parabolic and Hyperbolic Problems, FVCA 7,*

*Springer,*

**2014**

*, 78*, 703-711.

**Rybak, I. & Magiera, J.:**A multiple-time-step technique for coupled free flow and porous medium systems,

*J. Comput. Phys.,*

**2014**

*, 272*, 327-342.

**Wendland, W. L.:**Martin Costabel's version of the trace theorem revisited,

*Math. Methods Appl. Sci.,*

**2014**

*, 37 (13)*, 1924-1955.

**Wirtz, D.; Sorensen, D. & Haasdonk, B.:**A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems,

*SIAM Journal on Scientific Computing,*

*Society for Industrial & Applied Mathematics (SIAM),*

**2014**

*, 36*, A311-A338.

**Wirtz, D.; Sorensen, D. & Haasdonk, B.:**A-posteriori error estimation for DEIM reduced nonlinear dynamical systems,

*SIAM J. Sci. Comp.,*

*University of Stuttgart,*

**2014**

*, 36*, A311-A338.

*Fuhrmann, Jürgen and Ohlberger, Mario and Rohde, Christian*

*(Eds.)*, Finite Volumes for Complex Applications VII Elliptic, Parabolic and Hyperbolic Problems, FVCA 7, Berlin, June 2014,

**2014**

*, Vol. 77/78*.

## 2013

**Dihlmann, M. & Haasdonk, B.:**Certified Nonlinear Parameter Optimization with Reduced Basis Surrogate Models,

*PAMM, Proc. Appl. Math. Mech., Special Issue: 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Novi Sad 2013; Editors: L. Cvetković, T. Atanacković and V. Kostić,*

**2013**

*, 13*, 3-6.

**Eck, C.; Kutter, M.; Sändig, A.-M. & Rohde, C.:**A two scale model for liquid phase epitaxy with elasticity: An iterative procedure,

*ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik,*

*WILEY-VCH Verlag,*

**2013**

*, 93*, 745-761.

**Eisenschmidt, K.; Rauschenberger, P.; Rohde, C. & Weigand, B.:**Modelling of freezing processes in super-cooled droplets on sub-grid scale,

*ILASS–Europe, 25th European Conference on Liquid Atomization and Spray Systems,*

**2013**.

**Fechter, S.; Jägle, F. & Schleper, V.:**Exact and approximate Riemann solvers at phase boundaries,

*Computers & Fluids,*

**2013**

*, 75*, 112-126.

**Fericean, D.; Grosan, T.; Kohr, M. & Wendland, W. L.:**Interface boundary value problems of Robin-transmission type for the Stokes and Brinkman systems on n-dimensional Lipschitz domains: Applications,

*Math. Methods Appl. Sci.,*

**2013**

*, 36*, 1631-1648.

**Fericean, D. & Wendland, W. L.:**Layer potential analysis for a Dirichlet-transmission problem in Lipschitz domains in R^n,

*ZAMM,*

**2013**

*, 93*, 762-776.

**Göttlich, S.; Hoher, S.; Schindler, P.; Schleper, V. & Verl, A.:**Modeling, simulation and validation of material flow on conveyor belts,

*Appl. Math. Modell.,*

**2013**

*, 38*, 3295-3313.

**Giesselmann, J.:**Cavitation and Singular Solutions in Nonlinear Elastodynamics,

*PAMM 13,*

*Wiley,*

**2013**, 363-364.

**Giesselmann, J.; Miroshnikov, A. & Tzavaras, A. E.:**The problem of dynamic cavitation in nonlinear elasticity,

*Séminaire Laurent Schwartz — EDP et applications,*

**2013**.

**Kaulmann, S. & Haasdonk, B.:**

*Moitinho de Almeida, José Paulo Baptista and Diez, Pedro and Tiago, Carlos and Parés, Núria*

*(Eds.)*, Online Greedy Reduced Basis Construction Using Dictionaries,

*VI International Conference on Adaptive Modeling and Simulation (ADMOS 2013),*

**2013**, 365-376.

**Kissling, F. & Karlsen, K.:**On the singular limit of a two-phase flow equation with heterogeneities and dynamic capillary pressure,

*ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik,*

*WILEY-VCH Verlag,*

**2013**, n/a-n/a.

**Kohr, M.; Lanza de Cristoforis, M. & Wendland, W. L.:**Nonlinear Neumann-Transmission Problems for Stokes and Brinkman Equations on Euclidean Lipschitz Domains,

*Potential Analysis,*

**2013**

*, 38*, 1123-1171.

**Kohr, M.; Pintea, C. & Wendland, W. L.:**Dirichlet-transmission problems for pseudodifferential Brinkman operators on Sobolev and Besov spaces associated to Lipschitz domains in Riemannian manifolds,

**2013**

*, 93*, 446-458.

**Kohr, M.; Pintea, C. & Wendland, W. L.:**Layer Potential Analysis for Pseudodifferential Matrix Operators in Lipschitz Domains on Compact Riemannian Manifolds: Applications to Pseudodifferential Brinkman Operators,

*International Mathematics Research Notices,*

**2013**

*, 2013 (19)*, 4499-4588.

**Moutari, S.; Herty, M.; Klein, A.; Oeser, M.; Schleper, V. & Steinaur, G.:**Modeling road traffic accidents using macroscopic second-order models of traffic flow,

*IMA Journal of Applied Mathematics,*

**2013**

*, 78*, 1087-1108.

**Redeker, M. & Eck, C.:**A fast and accurate adaptive solution strategy for two-scale models with continuous inter-scale dependencies,

*Journal of Computational Physics,*

**2013**

*, 240*, 268-283.

**Rohde, C.; Wang, W. & Xie, F.:**Decay Rates to Viscous Contact Waves for a 1D Compressible Radiation Hydrodynamics Model,

*Mathematical Models and Methods in Applied Sciences,*

**2013**

*, 23*, 441-469.

**Rohde, C.; Wang, W. & Xie, F.:**Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves,

*Communications on Pure and Applied Analysis,*

**2013**

*, 12*, 2145-2171.

**Wirtz, D. & Haasdonk, B.:**An Improved Vectorial Kernel Orthogonal Greedy Algorithm,

*Dolomites Research Notes on Approximation,*

**2013**

*, 6*, 83-100.

**Yannou, B.; Cluzel, F. & Dihlmann, M.:**Evolutionary and interactive sketching tool for innovative car shape design,

*Machanics & Industry,*

**2013**

*, 14*, 1-22.

## 2012

**Aki, G. L.; Daube, J.; Dreyer, W.; Jan Giesselmann; Kränkel, M. & Kraus, C.:**A diffuse interface model for quasi-incompressible flows : Sharp interface limits and numerics,

*ESAIM Proceedings Vol. 38,*

**2012**, 54-77.

**Audusse, E.; Berthon, C.; Chalons, C.; Delestre, O.; Goutal, N.; Jodeau, M.; Jaques Sainte-Marie; Giesselmann, J. & Sadaka, G.:**Sediment transport modelling : Relaxation schemes for Saint-Venant - Exner and three layer models,

*ESAIM Proceedings Vol. 38,*

**2012**, 78-98.

**Chalons, C.; Coquel, F.; Engel, P. & Rohde, C.:**Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems,

*SIAM Journal on Scientific Computing,*

**2012**

*, 34*, A1753-A1776.

**Colombo, R. M. & Schleper, V.:**Two-phase flows: non-smooth well posedness and the compressible to incompressible limit,

*Nonlinear Anal. Real World Appl.,*

**2012**

*, 13*, 2195-2213.

**Corli, A. & Rohde, C.:**Singular limits for a parabolic-elliptic regularization of scalar conservation laws,

*J. Differential Equations,*

**2012**

*, 253*, 1399-1421.

**Dihlmann, M.; Kaulmann, S. & Haasdonk, B.:**Online Reduced Basis Construction Procedure for Model Reduction of Parametrized Evolution Systems,

*Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling,*

**2012**.

**Dreyer, W.; Giesselmann, J.; Kraus, C. & Rohde, C.:**Asymptotic Analysis for Korteweg Models,

*Interfaces Free Bound.,*

**2012**

*, 14*, 105 - 143.

**Engel, P. & Rohde, C.:**

*T. Li and S. Jiang*

*(Eds.)*, On the Space-Time Expansion Discontinuous Galerkin Method,

*Hyperbolic Problems: Theory, Numerics and Applications,*

**2012**, 406-414.

**Feistauer, M. & Sändig, A.-M.:**Graded mesh refinement and error estimates of higher order for DGFE solutions of elliptic boundary value problems in polygons,

*Numerical Methods for Partial Differential Equations,*

*Wiley Subscription Services, Inc., A Wiley Company,*

**2012**

*, 28*, 1124-1151.

**Giesselmann, J.:**

*T. Li and S. Jiang*

*(Eds.)*, Sharp interface limits for Korteweg Models,

*Hyperbolic Problems: Theory, Numerics, Applications,*

**2012**

*, 2*, 422 - 430.

**Giesselmann, J. & Wiebe, M.:**

*E. Vasquez-Cendon, A. Hidalgo, P. Garcia Navarro, L. Cea*

*(Eds.)*, Finite volume schemes for balance laws on time-dependent surfaces,

*Numerical Methods for Hyperbolic Equations,*

*Taylor and Francis Group,*

**2012**.

**Häcker, A.:**A mathematical model for mesenchymal and chemosensitive cell dynamics,

*Journal of mathematical Biology,*

**2012**

*, 64*, 361-401.

**Harbrecht, H.; Wendland, W. L. & Zorii, N.:**On Riesz minimal energy problems,

*J. Math. Anal. Appl.,*

**2012**

*, 393*, 397-412.

**Hoher, S.; Schindler, P.; G?ttlich, S.; Schleper, V. & Röck, S.:**

*ElMaraghy, Hoda A.*

*(Eds.)*, System Dynamic Models and Real-time Simulation of Complex Material Flow Systems,

*Enabling Manufacturing Competitiveness and Economic Sustainability,*

*Springer Berlin Heidelberg,*

**2012**, 316-321.

**Jackson, A. S.; Rybak, I.; Helmig, R.; Gray, W. G. & Miller, C. T.:**Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 9. Transition region models,

*Adv. Water Res.,*

**2012**

*, 42*, 71-90.

**Jaegle, F.; Rohde, C. & Zeiler, C.:**A multiscale method for compressible liquid-vapor flow with surface tension,

*ESAIM: Proc.,*

**2012**

*, 38*, 387-408.

**Kelkel, J. & Surulescu, C.:**A Multiscale Approach to Cell Migration in Tissue Networks,

*Mathematical Models and Methods in Applied Sciences,*

**2012**

*, 22*, 1150017.

**Kissling, F.; Helmig, R. & Rohde, C.:**Simulation of Infiltration Processes in the Unsaturated Zone Using a Multi-Scale Approach,

*Vadose Zone J.,*

**2012**

*, 11*, -.

**Kissling, F. & Rohde, C.:**

*T. Li and S. Jiang*

*(Eds.)*, Numerical Simulation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method,

*Hyperbolic Problems: Theory, Numerics and Applications,*

**2012**, 469-478.

**Kohr, M.; Pintea, C. & Wendland, W. L.:**Potential analysis for pseudodifferential matrix operators in Lipschitz domains on Riemannian manifolds: Applications to Brinkman operators.,

*Mathematica,*

**2012**

*, 54*, 159-176.

**Kohr, M.; Raja Sekhar, G. P.; Ului, E. M. & Wendland, W. L.:**Two-dimensional Stokes-Brinkman cell model---a boundary integral formulation,

*Appl. Anal.,*

**2012**

*, 91*, 251-275.

**Kröker, I. & Rohde, C.:**Finite volume schemes for hyperbolic balance laws with multiplicative noise,

*Appl. Numer. Math.,*

**2012**

*, 62*, 441-456.

**Richter, T.; Rudlof, S.; Adjibadji, B.; Bernlöhr, H.; Grüninger, C.; Munz, C.-D.; Stock, A.; Rohde, C. & Helmig, R.:**ViPLab: a virtual programming laboratory for mathematics and engineering,

*Interactive Technology and Smart Education,*

**2012**

*, 9*, 246 - 262.

**Rohde, C. & Xie, F.:**Global existence and blowup phenomenon for a 1D radiation hydrodynamics model problem,

*Math. Methods Appl. Sci.,*

**2012**

*, 35*, 564-573.

**Schleper, V.:**

*Vazquez-Cendon, E. and Hidalgo, A. and Garcia-Navarro, P. and Cea, L.*

*(Eds.)*, On the coupling of compressible and incompressible fluids,

*Numerical Methods for Hyperbolic Equations,*

*Taylor & Francis Group,*

**2012**.

**Steinhorst, P. & Sändig, A.-M.:**Reciprocity principle for the detection of planar cracks in anisotropic elastic material,

*Inverse Problems,*

**2012**

*, 28*, 085010.

**Waldherr, S. & Haasdonk, B.:**Efficient Parametric Analysis of the Chemical Master Equation through Model Order Reduction,

*BMC Systems Biology,*

**2012**

*, 6*, 81.

**Winkel, C.; Neumann, S.; Surulescu, C. & Scheurich, P.:**A minimal mathematical model for the initial molecular interactions of death receptor signalling,

*Math. Biosci. Eng.,*

**2012**

*, 9*, 663-683.

**Wirtz, D. & Haasdonk, B.:**A-posteriori error estimation for parameterized kernel-based systems,

*Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling,*

**2012**.

**Wirtz, D. & Haasdonk, B.:**Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems,

*Systems and Control Letters,*

**2012**

*, 61*, 203 - 211.

*F. Coquel and M. Gutnic and P. Helluy and F. Lagoutière and C. Rohde and N. Seguin*

*(Eds.)*, CEMRACS 2011, Multiscale Coupling of Complex Models,

*ESAIM Proceedings,*

**2012**

*, 38*.

## 2011

**Bürger, R.; Kröker, I. & Rohde, C.:**Uncertainty quantification for a clarifier-thickener model with random feed,

*Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2,*

*Springer,*

**2011**

*, 4*, 195-203.

**Dihlmann, M.; Drohmann, M. & Haasdonk, B.:**Model Reduction of Parametrized Evolution Problems using the Reduced basis Method with Adaptive Time-Partitioning,

*Proc. of ADMOS 2011,*

**2011**.

**Herty, M. & Schleper, V.:**Traffic flow with unobservant drivers,

*ZAMM Z. Angew. Math. Mech.,*

**2011**

*, 91*, 763-776.

**Herty, M. & Schleper, V.:**Time discretizations for numerical optimisation of hyperbolic problems,

*Appl. Math. Comput.,*

**2011**

*, 218*, 183-194.

**Kabil, B.:**On the asymptotics of solutions to resonator equations,

*Hyperbolic Problems: Theory, Numerics, Applications,*

**2011**

*, 8*, 373-380.

**Kaulmann, S.; Ohlberger, M. & Haasdonk, B.:**A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems,

*Comptes Rendus Mathematique,*

**2011**

*, 349*, 1233-1238.

**Kelkel, J. & Surulescu, C.:**On a stochastic reaction--diffusion system modeling pattern formation on seashells,

*Mathematical Biosciences and Engineering,*

*Springer-Verlag,*

**2011**

*, 8*, 575-589.

**Kohr, M.; Pintea, C. & Wendland, W. L.:**Dirichlet-transmission problems for general Brinkman operators on Lipschitz and $C^1$ domains in Riemannian manifolds,

*Discrete Contin. Dyn. Syst. Ser. B,*

**2011**

*, 15*, 999-1018.

**Kutter, M. & Sändig, A.-M.:**Modeling of ferroelectric hysteresis as variational inequality,

*GAMM-Mitteilungen,*

*WILEY-VCH Verlag,*

**2011**

*, 34*, 84-89.

**Lalegname, A. & Sändig, A.:**Wave-crack interaction in finite elastic bodies,

*International Journal of Fracture,*

*Springer Netherlands,*

**2011**

*, 172*, 131-149.

**Mel'nyk, T. A.; Nakvasiuk, I. A. & Wendland, W. L.:**Homogenization of the Signorini boundary-value problem in a thick junction and boundary integral equations for the homogenized problem,

*Math. Methods Appl. Sci.,*

**2011**

*, 34*, 758-775.

**Mosthaf, K.; Baber, K.; Flemisch, B.; Helmig, R.; Leijnse, A.; Rybak, I. & Wohlmuth, B.:**A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow,

*Water Resour. Res.,*

**2011**

*, 47*, W10522.

**Rössle, A. & Sändig, A.-M.:**Corner Singularities and Regularity Results for the Reissner/Mindlin Plate Model,

*Journal of Elasticity,*

*Springer Netherlands,*

**2011**

*, 103*, 113-135.

**Richter, T.; Rudlof, S.; Adjibadji, B.; Berlohr, H.; Gruninger, C.; Munz, C.-D.; Rohde, C. & Helmig, R.:**ViPLab - A Virtual Programming Laboratory for Mathematics and Engineering,

*Proceedings of the 2011 IEEE International Symposium on Multimedia,*

*IEEE Computer Society,*

**2011**, 537-542.

**Wendland, W. L.:**Boundary element domain decomposition with Trefftz elements and Levi fuctions,

*19th Intern. Conf. on Computer Methods in Mechanics,*

*Publ. House of Warsaw Univ. Technology,*

**2011**.

## 2010

**Kelkel, J. & Surulescu, C.:**On a stochastic reaction--diffusion system modeling pattern formation on seashells,

*Journal of Mathematical Biology,*

*Springer-Verlag,*

**2010**

*, 60*, 765-796.

**Kissling, F. & Rohde, C.:**The Computation of Nonclassical Shock Waves with a Heterogeneous Multiscale Method,

*Netw. Heterog. Media,*

**2010**

*, 5*, 661-674.

**Rohde, C.:**A local and low-order Navier-Stokes-Korteweg system,

*Nonlinear partial differential equations and hyperbolic wave phenomena,*

*Amer. Math. Soc.,*

**2010**

*, 526*, 315-337.