Publications

F. Musco and A. Barth, “Deep learning methods for stochastic Galerkin approximations of elliptic random PDEs,” 2024. [Online]. Available: https://arxiv.org/abs/2409.08063

A. Barth and A. Stein, “A stochastic transport problem with Lévy noise: Fully discrete numerical approximation.,” 2023. [Online]. Available: https://arxiv.org/abs/1910.14657

L. Brencher and A. Barth, “Scalar conservation laws with stochastic discontinuous flux function,” 2022. doi: 10.48550/arXiv.2107.00549.

A. Barth and A. Stein, “A stochastic transport problem with Lévy noise: Fully discrete numerical approximation.,” Mathematics and Computers in Simulation, vol. 227, pp. 347–370, 2025, [Online]. Available: https://doi.org/10.1016/j.matcom.2024.07.036

C. Beschle and A. Barth, “Complexity analysis of quasi continuous level Monte Carlo,” ESAIM: Mathematical Modelling and Numerical Analysis, 2024, doi: 10.1051/m2an/2024039.

C. A. Beschle and A. Barth, “Quasi continuous level Monte Carlo for random elliptic PDEs,” in Hinrichs, A., Kritzer, P., Pillichshammer, F. (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2022, vol. 460, in Hinrichs, A., Kritzer, P., Pillichshammer, F. (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2022, vol. 460. , Springer Proceedings in Mathematics & Statistics, 2024, pp. 3–31. doi: 10.1007/978-3-031-59762-6_1.

F. Musco and A. Barth, “Deep learning methods for stochastic Galerkin approximations of elliptic random PDEs,” 2024. [Online]. Available: https://arxiv.org/abs/2409.08063

A. Barth and A. Stein, “A stochastic transport problem with Lévy noise: Fully discrete numerical approximation.,” 2023. [Online]. Available: https://arxiv.org/abs/1910.14657

C. A. Beschle and A. Barth, “Quasi continuous level Monte Carlo for random elliptic PDEs,” 2023.

R. Merkle and A. Barth, “On Properties and Applications of Gaussian Subordinated Lévy Fields,” Methodology and computing in applied probability, vol. 25, pp. 1–33, 2023, doi: 10.1007/s11009-023-10033-2.

C. Beschle and A. Barth, “Uncertainty visualization: Fundamentals and recent developments, code to produce data and visuals used in Section 5,” 2022. doi: 10.18419/darus-3154.

C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces,” Numerische Mathematik, vol. 151, no. 1, Art. no. 1, 2022, doi: 10.1007/s00211-022-01280-5.

D. Hägele et al., “Uncertainty visualization : Fundamentals and recent developments,” Information technology, vol. 64, no. 4–5, Art. no. 4–5, 2022, doi: 10.1515/itit-2022-0033.

L. Mehl, C. Beschle, A. Barth, and A. Bruhn, “Replication Data for: An Anisotropic Selection Scheme for Variational Optical Flow Methods with Order-Adaptive Regularisation,” 2022. doi: 10.18419/darus-2890.

R. Merkle and A. Barth, “On Some Distributional Properties of Subordinated Gaussian Random Fields,” Methodology and computing in applied probability, 2022, doi: 10.1007/s11009-022-09958-x.

R. Merkle and A. Barth, “Subordinated Gaussian random fields in elliptic partial differential equations,” Stochastics and partial differential equations, 2022, doi: 10.1007/s40072-022-00246-w.

R. Merkle and A. Barth, “Multilevel Monte Carlo estimators for elliptic PDEs with Lévy-type diffusion coefficient,” BIT - numerical mathematics, 2022, doi: 10.1007/s10543-022-00912-4.

L. Mehl, C. Beschle, A. Barth, and A. Bruhn, “An Anisotropic Selection Scheme for Variational Optical Flow Methods with Order-Adaptive Regularisation,” Proceedings of the International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), pp. 140--152, 2021, doi: 10.1007/978-3-030-75549-2_12.

L. Brencher and A. Barth, “Hyperbolic Conservation Laws with Stochastic Discontinuous Flux Functions,” in Finite Volumes for Complex Applications IX : Methods, Theoretical Aspects, Examples, R. Klöfkorn, E. Keilegavlen, F. A. Radu, and J. Fuhrmann, Eds., in Finite Volumes for Complex Applications IX : Methods, Theoretical Aspects, Examples. Springer, 2020, pp. 265–273. doi: 10.1007/978-3-030-43651-3_23.

A. Stein, “Uncertainty quantification with Lévy-type random fields,” Dissertation, Universität Stuttgart, Stuttgart, 2020. doi: 10.18419/opus-11082.

M. Köppel et al., “Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage,” 2019. [Online]. Available: https://zenodo.org/records/933827

A. Barth and I. Kröker, “Finite Volume Methods for Hyperbolic Partial Differential Equations with Spatial Noise,” in Theory, Numerics and Applications of Hyperbolic Problems I, C. Klingenberg and M. Westdickenberg, Eds., in Theory, Numerics and Applications of Hyperbolic Problems I. Cham: Springer International Publishing, 2018, pp. 125--135.

A. Barth and A. Stein, “Approximation and simulation of infinite-dimensional Lévy processes,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 6, pp. 286–334, 2018, doi: 10.1007/s40072-017-0109-2.

A. Barth and T. Stüwe, “Weak convergence of Galerkin approximations of stochastic partial  differential equations driven by additive Lévy noise,” Mathematics and Computers in Simulation, vol. 143, pp. 215--225, 2018, doi: 10.1016/j.matcom.2017.03.007.

A. Barth and F. G. Fuchs, “Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients,” Applied numerical mathematics, vol. 121, pp. 38–51, Nov. 2017, doi: 10.1016/j.apnum.2017.06.009.

A. Barth, B. Harrach, N. Hyvönen, and L. Mustonen, “Detecting stochastic inclusions in electrical impedance tomography,” Inverse problems, vol. 33, no. 11, Art. no. 11, 2017, doi: 10.1088/1361-6420/aa8f5c.

A. Barth, R. Burger, I. Kröker, and C. Rohde, “Computational uncertainty quantification for a clarifier-thickener model    with several random perturbations: A hybrid stochastic Galerkin approach,” COMPUTERS & CHEMICAL ENGINEERING, vol. 89, pp. 11–26, Jun. 2016, doi: 10.1016/j.compchemeng.2016.02.016.

A. Barth, C. Schwab, and J. Sukys, “Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier--Stokes Equations,” in Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, R. Cools and D. Nuyens, Eds., in Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014. Cham: Springer International Publishing, 2016, pp. 209--227. doi: 10.1007/978-3-319-33507-0_8.

A. Barth and S. Moreno-Bromberg, “Optimal risk and liquidity management with costly refinancing opportunities,” Insurance Math. Econom., vol. 57, pp. 31–45, 2014, doi: 10.1016/j.insmatheco.2014.05.001.

A. Abdulle, A. Barth, and C. Schwab, “Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs,” Multiscale modeling & simulation, vol. 11, no. 4, Art. no. 4, 2013, doi: 10.1137/120894725.

A. Barth, A. Lang, and C. Schwab, “Multilevel Monte Carlo method for parabolic stochastic partial differential equations,” BIT : numerical mathematics, vol. 53, no. 1, Art. no. 1, 2013, doi: 10.1007/s10543-012-0401-5.

A. Barth and A. Lang, “Multilevel Monte Carlo method with applications to stochastic partial differential equations,” International journal of computer mathematics, vol. 89, no. 18, Art. no. 18, 2012, doi: 10.1080/00207160.2012.701735.

A. Barth, F. E. Benth, and J. Potthoff, “Hedging of spatial temperature risk with market-traded futures,” Appl. Math. Finance, vol. 18, no. 2, Art. no. 2, 2011, doi: 10.1080/13504861003722385.

A. Barth, C. Schwab, and N. Zollinger, “Multi-level Monte Carlo Finite Element Method for Elliptic PDEs with Stochastic Coefficients.,” Numerische Mathematik, vol. 119, pp. 123–161, 2011, doi: 10.1007/s00211-011-0377-0.

A. Barth, “A finite element method for martingale-driven stochastic partial differential equations,” Communications on Stochastic Analysis, vol. 4, no. 3, Art. no. 3, 2010, doi: 10.31390/cosa.4.3.04.

A. Barth, “Stochastic Partial Differential Equations: Approximations and Applications,” Dissertation, University of Oslo, 2009. [Online]. Available: http://urn.nb.no/URN:NBN:no-24072