Publications

Find publications and preprints authored by people from our working group

  1. 2019

    1. Langer, A., & Gaspoz, F. Overlapping domain decomposition methods for total variation denoising Retrieved from http://people.ricam.oeaw.ac.at/a.langer/publications/DDfTV_2preprint.pdf.
  2. 2018

    1. Hintermüller, M., Langer, A., Rautenberg, C. N., & Wu, T. Adaptive regularization for reconstruction from subsampled data. In X.-C. Tai, E. Bae, & M. Lysaker (Eds.), Imaging, Vision and Learning Based on Optimization and PDEs. Bergen: Springer International Publishing doi:10.1007/978-3-319-91274-5_1.
    2. Alkämper, M., Gaspoz, F., & Klöfkorn, R. A Weak Compatibility Condition for Newest Vertex    Bisection in Any Dimension. SIAM Journal on Scientific Computing, 40(6), A3853–A3872.
    3. Langer, A. Locally adaptive total variation for removing mixed Gaussian-impulse noise. International Journal of Computer Mathematics, 19.
    4. Langer, A. Investigating the influence of box-constraints on the solution of a total variation model via an efficient primal-dual method. Journal of Imaging, 4, 1.
  3. 2017

    1. Langer, A. Automated Parameter Selection for Total Variation Minimization in Image Restoration. Journal of Mathematical Imaging and Vision, 57, 239--268.
    2. Langer, A. Automated Parameter Selection in the $L^1$-$L^2$-TV Model for Removing Gaussian Plus Impulse Noise. Inverse Problems, 33, 41.
    3. Alkämper, M., & Langer, A. Using DUNE-ACFem for Non-smooth Minimization of Bounded Variation Functions. Archive of Numerical Software, 5(1), 3--19.
    4. Gaspoz, F. D., Kreuzer, C., Siebert, K., & Ziegler, D. A convergent time-space adaptive $dG(s)$ finite element method for parabolic problems motivated by equal error distribution Retrieved from https://arxiv.org/abs/1610.06814.
    5. Gaspoz, F. D., Morin, P., & Veeser, A. A posteriori error estimates with point sources in fractional sobolev spaces. Numerical Methods for Partial Differential Equations, 33(4), 1018--1042.
    6. Alkämper, M., & Klöfkorn, R. Distributed Newest Vertex Bisection. Journal of Parallel and Distributed Computing, 104, 1-- 11.
    7. Hintermüller, M., Rautenberg, C. N., Wu, T., & Andreas Langer. Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II: Algorithm, Its Analysis and Numerical Tests. Journal of Mathematical Imaging and Vision, 1--19.
  4. 2016

    1. Alkämper, M., Dedner, A., Klöfkorn, R., & Martin Nolte. The DUNE-ALUGrid Module. Archive of Numerical Software, 4(1), 1--28.
    2. Gaspoz, F. D., Heine, C.-J., & Siebert, K. G. Optimal Grading of the Newest Vertex Bisection and H1-Stability of the L2-Projection. IMA Journal of Numerical Analysis, 36(3), 1217--1241.
  5. 2015

    1. Hintermüller, M., & Langer, A. Non-overlapping domain decomposition methods for dual total variation based image denoising. Journal of Scientific Computing, 62(2), 456--481.
  6. 2014

    1. Hintermüller, M., & Langer, A. Adaptive Regularization for Parseval Frames in Image Processing. SFB-Report No. 2014-014 Retrieved from http://people.ricam.oeaw.ac.at/a.langer/publications/SFB-Report-2014-014.pdf.
    2. Kohls, K., Rösch, A., & Siebert, K. G. A Posteriori Error Analysis of Optimal Control Problems with Control Constraints. SIAM J. Control Optim., 52(3), 1832--1861. (30 pages).
    3. Hintermüller, M., & Langer, A. Surrogate Functional Based Subspace Correction Methods for Image Processing. In Domain Decomposition Methods in Science and Engineering XXI (pp. 829--837). Springer.
    4. Gaspoz, F. D., & Morin, P. Approximation classes for adaptive higher order finite element approximation. Mathematics of Computation, 83(289), 2127--2160.
  7. 2013

    1. Heine, C.-J., Möller, C. A., Peter, M. A., & Siebert, K. G. Multiscale adaptive simulations of concrete carbonation taking into account the evolution of the microstructure. In C. Hellmich, B. Pichler, & D. Adam (Eds.), Poromechanics (Vol. V, pp. 1964--1972). ASCE.
    2. Hintermüller, M., & Langer, A. Subspace Correction Methods for a Class of Nonsmooth and Nonadditive Convex Variational Problems with Mixed $L^1$/$L^2$ Data-Fidelity in Image Processing. SIAM Journal on Imaging Sciences, 6(4), 2134--2173.
    3. Langer, A., Osher, S., & Schönlieb, C.-B. Bregmanized domain decomposition for image restoration. Journal of Scientific Computing, 54(2), 549--576.
  8. 2012

    1. Fornasier, M., Kim, Y., Langer, A., & Schönlieb, C.-B. Wavelet Decomposition Method for $L_2$/TV-Image Deblurring. SIAM Journal on Imaging Sciences, 5(3), 857--885.
    2. Siebert, K. G. Mathematically Founded Design of Adaptive Finite Element Software. In Multiscale and Adaptivity: Modelling, Numerics and Applications (Vol. 2040, pp. 227--309). Berlin: Springer.
    3. Kohls, K., Rösch, A., & Siebert, K. G. A Posteriori Error Estimators for Control Constrained Optimal Control Problems. In L. et al (Ed.), Constrained Optimiziation and Optimal Control for Partial Differential Equations (Vol. 160, pp. 431--443). Springer.
  9. 2011

    1. Kreuzer, C., & Siebert, K. G. Decay Rates of Adaptive Finite Elements with Dörfler Marking. Numerische Mathematik, 117(4), 679--716.
    2. Siebert, K. G. A Convergence Proof for Adaptive Finite Elements without Lower Bound. IMA Journal of Numerical Analysis, 31(3), 947--970.
  10. 2010

    1. Kohls, K., Rösch, A., & Siebert, K. G. Analysis of Adaptive Finite Elements for Constrained Optimal Control Problems doi:10.4171/OWR/2010/07.
    2. Fornasier, M., Langer, A., & Schönlieb, C.-B. A convergent overlapping domain decomposition method for total variation minimization. Numerische Mathematik, 116(4), 645--685.
    3. Deckelnick, K., Dziuk, G., Elliott, C. M., & Heine, C.-J. An $h$-narrow band finite-element method for elliptic equations on implicit surfaces. IMA J. Numer. Anal., 30(2), 351--376.
  11. 2009

    1. Fornasier, M., Langer, A., & Schönlieb, C.-B. Domain decomposition methods for compressed sensing. In Proceedings of the International Conference of SampTA09 Retrieved from http://arxiv.org/abs/0902.0124.
    2. Gaspoz, F. D., & Morin, P. Convergence rates for adaptive finite elements. IMA Journal on Numerical Analysis, 29(4), 917--936.
    3. Nochetto, R. H., Siebert, K. G., & Veeser, A. Theory of Adaptive Finite Element Methods: An Introduction. In R. A. DeVore & A. Kunoth (Eds.), Multiscale, Nonlinear and Adaptive Approximation (pp. 409--542). Springer.
  12. 2008

    1. Heine, C.-J. Finite element methods on unfitted meshes. Preprint Fak. f. Math. Phys. Univ. Freiburg, (8).
    2. Köster, D., Kriessl, O., & Siebert, K. G. Design of Finite Element Tools for Coupled Surface and Volume Meshes. Numerical Mathematics: Theory, Methods and Applications, 1(3), 245--274.
    3. Antil, H., Gantner, A., Hoppe, R. H. W., Köster, D., Siebert, K. G., & Wixforth, A. Modeling and Simulation of Piezoelectrically Agitated Acoustic Streaming on Microfluidic Bio\textbackslash-chips. In L. et al (Ed.), Domain Decomposition Methods in Science and Engineering XVII (Vol. 60, pp. 305--312). Springer.
    4. Cascón, J. M., Kreuzer, C., Nochetto, R. H., & Siebert, K. G. Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method. SIAM Journal on Numerical Analysis, 46(5), 2524--2550.
    5. Morin, P., Siebert, K. G., & Veeser, A. A Basic Convergence Result for Conforming Adaptive Finite Elements. Mathematical Models and Methods in Applied Science, 18, 707--737.
  13. 2007

    1. Cascón, J. M., Kreuzer, C., Nochetto, R. H., & Siebert, K. G. Optimal Cardinality of an Adaptive Finite Element Method doi:10.4171/OWR/2007/29.
    2. Ganter, A., Hoppe, R. H. W., Köster, D., Siebert, K. G., & Wixforth, A. Numerical Simulation of Piezoelectrically Agitated Surface Acoustic Waves on Microfluidic Biochips. Computing and Visualization in Science, 10(3), 145--161.
    3. Morin, P., Siebert, K. G., & Veeser, A. Convergence of Finite Elements Adapted for Weaker Norms. In V. Cutello, G. Fotia, & L. Puccio (Eds.), Applied and Industrial Matematics in Italy - II (Vol. 75, pp. 468--479). Hackensack, NJ: World Sci. Publ.
    4. Morin, P., Siebert, K. G., & Veeser, A. Basic Convergence Results for Conforming Adaptive Finite Elements. Proceedings in Applied Mathematics and Mechanics, 7(1), 1026001--1026002.
    5. Cascón, J. M., Nochetto, R. H., & Siebert, K. G. Design and Convergence of AFEM in $H^div$. Mathematical Models & Methods in Applied Sciences, 17(11), 1849--1881.
    6. Morin, P., Siebert, K. G., & Veeser, A. A Basic Convergence Result for Conforming Adaptive Finite Element Methods doi:10.4171/OWR/2007/29.
    7. Siebert, K. G., & Veeser, A. A Unilaterally Constrained Quadratic Minimization with Adaptive Finite Elements. SIAM Journal on Optimization, 18(1), 260--289.
  14. 2006

    1. Nochetto, R. H., Schmidt, A., Siebert, K. G., & Veeser, A. Pointwise A Posteriori Error Estimates for Monotone Semi-linear Equations. Numerische Mathematik, 104(4), 515--538.
    2. Heine, C.-J. Computations of form and stability of rotating drops with finite elements. IMA J. Numer. Anal., 26(4), 723--751.
  15. 2005

    1. Siebert, K. G., & Veeser, A. Convergence of the Equidistribution Strategy doi:10.4171/OWR/2005/37.
    2. Schmidt, A., & Siebert, K. G. Design of Adaptive Finite Element Software. The Finite Element Toolbox ALBERTA. (B. T.J., M. Griebel, D. E. Keyes, R. M. Nieminen, D. Roose, & T. Schlick, Eds.)Lecture Notes in Computational Science and Engineering (Vol. 42). Berlin: Springer doi:10.1007/b138692.
    3. Nochetto, R. H., Siebert, K. G., & Veeser, A. Fully Localized A Posteriori Error Estimators and Barrier Sets for Contact Problems. SIAM Journal on Numerical Analysis, 42(5), 2118--2135.
  16. 2004

    1. Heine, C.-J. Isoparametric finite element approximation of curvature on hypersurfaces. Preprint Fak. f. Math. Phys. Univ. Freiburg, (26).
    2. Bamberger, A., Bänsch, E., & Siebert, K. G. Experimental and numerical investigation of edge tones. ZAMM Journal of Applied Mathematics and Mechanics, 84(9), 632--646.
  17. 2003

    1. Boschert, S., Schmidt, A., Siebert, K. G., Bänsch, E., Dziuk, G., Benz, K.-W., & Kaiser, T. Simulation of Industrial Crystal Growth by the Vertical Bridgman Method.
    2. Nochetto, R. H., Siebert, K. G., & Veeser, A. Pointwise A Posteriori Error Control for Elliptic Obstacle Problems. Numerische Mathematik, 95(1), 163--195.
    3. Dörfler, W., & Siebert, K. G. An Adaptive Finite Element Method for Minimal Surfaces. In H. K. S. Hildebrandt (Ed.), Geometric Analysis and Nonlinear Partial Differential Equations (pp. 146--175). Springer.
    4. Haasdonk, B., Ohlberger, M., Rumpf, M., Schmidt, A., & Siebert, K. G. Multiresolution Visualization of Higher Order Adaptive Finite Element Simulations. Computing, 70(3), 181--204.
    5. Morin, P., Nochetto, R. H., & Siebert, K. G. Local Problems on Stars: A Posteriori Error Estimators, Convergence, and Performance. Mathematics of Computation, 72(243), 1067--1097.
    6. Heine, C.-J. Computations of form and stability of rotating drops with finite elements.
  18. 2002

    1. Lin, K.-M., Boschert, S., Dold, P., Benz, K. W., Kriessl, O., Schmidt, A., … Dziuk, G. Numerical Methods for Industrial Bridgman Growth of (Cd,Zn)Te. Journal of Crystal Growth, 237–239, 1736--1740.
    2. Morin, P., Nochetto, R. H., & Siebert, K. G. Convergence of Adaptive Finite Element Methods. SIAM Review, 44(4), 631--658.
  19. 2001

    1. Schmidt, A., & Siebert, K. G. \textbackslashtextsfALBERT — Software for Scientific Computations and Applications. Acta Mathematica Universitatis Comenianae, New Ser., 70(1), 105--122.
  20. 2000

    1. Boschert, S., Schmidt, A., & Siebert, K. G. Numerical Simulation of Crystal Growth by the Vertical Bridgman Method. In J. S. Szmyd & K. Suzuki (Eds.), Modelling of Transport Phenomena in Crystal Growth (Vol. 6, pp. 315--330). WIT Press.
    2. Deckelnick, K., & Siebert, K. G. $W^1,ınfty$-Convergence of the Discrete Free Boundary for Obstacle Problems. IMA Journal of Numerical Analysis, 20(3), 481--498.
    3. Schmidt, A., & Siebert, K. G. A Posteriori Estimators for the $h$-$p$ Version of the Finite Element Method in 1d. Applied Numerical Mathematics, 35(1), 43--66.
    4. Morin, P., Nochetto, R. H., & Siebert, K. G. Data Oscillation and Convergence of Adaptive FEM. SIAM Journal on Numerical Analysis, 38(2), 466--488.
  21. 1999

    1. Schmidt, A., & Siebert, K. G. Abstract Data Structures for a Finite Element Package: Design Principles of ALBERT. Journal of Applied Mathematics and Mechanics, 79(1), 49--52.
  22. 1998

    1. Boschert, S., Kaiser, T., Schmidt, A., Siebert, K. G., Benz, K.-W., & Dziuk, G. Global Simulation of (Cd,Zn)Te Single Crystal Growth by the Vertical Bridgman Technique. In S. N. Atluri & P. E. O’Donoghue (Eds.), Modeling and Simulation Based Engineering. Tech Science Press Retrieved from http://www.techscience.com/books/msbe_hc_rm.html.
    2. Schmidt, A., & Siebert, K. G. Concepts of the Finite Element Toolbox ALBERT.
    3. Siebert, K. G. Einführung in die numerische Behandlung der Navier-Stokes-Gleichungen.
  23. 1996

    1. Rumpf, M., Schmidt, A., & Siebert, K. G. Functions Defining Arbitrary Meshes — A Flexible Interface Between Numerical Data and Visualization Routines. Computer Graphics Forum, 15(2), 129--141.
    2. Siebert, K. G. An A Posteriori Error Estimator for Anisotropic Refinement. Numerische Mathematik, 73(3), 373--398.
    3. Schmidt, A., & Siebert, K. G. Numerical Aspects of Parabolic Free Boundary Problems - Adaptive Finite Element Methods.
  24. 1995

    1. Bänsch, E., & Siebert, K. G. A Posteriori Error Estimation for Nonlinear Problems by Duality Techniques.
    2. Rumpf, M., Schmidt, A., & Siebert, K. G. On a Unified Visualization Approach for Data from Advanced Numerical Methods. In P. Z. R. Scateni, J. Van Wijk (Ed.), Visualization in Scientific Computing ’95 (pp. 35--44). Springer.
  25. 1993

    1. Siebert, K. G. An A Posteriori Error Estimator for Anisotropic Refinement.
    2. Siebert, K. G. Local Refinement of 3D-Meshes Consisting of Prisms and Conforming Closure. IMPACT of Computing in Science and Engineering, 5(4), 271--284.
  26. 1990

    1. Siebert, K. G. Ein Finite-Elemente-Verfahren zur Lösung der inkompressiblen Euler-Gleichungen auf der Sphäre mit der Stromlinien-Diffusions-Methode.
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