Dr. Benjamin Dörich
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by appointment
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Kollegiengebäude Mathematik (20.30)
3.057
+49 721 608 46680
+49 721 608 43767
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benjamin.doerich@kit.edu
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Englerstr. 2
76131 Karlsruhe
Link to my Junior Research Group Numerical methods for nonlinear optics and to my ORCID and Google Scholar page..
Research interests
- Error analysis for the time and space discretization
- time integration by exponential integrators, Runge–Kutta, and multistep methods
- spatial discretization by finite elements
- rigorous error bounds
- Construction of tailor-made methods for specific applications
- treatment of nonlinear effects
- low-regularity requirements
Preprints
- B. Dörich: Approximation of minimizers of the Ginzburg--Landau energy in non-convex domains. Preprint
- R. Altmann, B. Dörich, and C. Zimmer: Gautschi-type and implicit--explicit integrators for constrained wave equations. Preprint
- J. Careaga, B. Dörich, and V. Nikolić: Finite element discretization of nonlinear models of ultrasound heating. Preprint
- C. Döding, B. Dörich, and P. Henning: A multiscale approach to the stationary Ginzburg–Landau equations of superconductivity Preprint
- B. Dörich and V. Nikolić: Robust fully discrete error bounds for the Kuznetsov equations in the inviscid limit. Preprint
Publications
- B. Dörich, J. Dörner, and M. Hochbruck: Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions. (accepted in Math. Comp.) Preprint
- S. Burkhard, B. Dörich, M. Hochbruck, and C. Lasser: Variational Gaussian approximation for the magnetic Schrödinger equation. J. Phys. A: Math. Theor. 57, 295202, 2024. Link, Preprint
- B. Dörich and P. Henning: Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-$\kappa$ regime. SIAM J. Numer. Anal., 62(3):1313–1343, 2024. Link, Preprint
- B. Dörich: Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions. Found. Comput. Math., 25:303–350, 2025. Link, Preprint
- B. Dörich, J. Leibold, and B. Maier: Maximum norm error bounds for the full discretization of non-autonomous wave equations. IMA J. Numer. Anal., 44(4):2480-2512, 2024 Link, Preprint
- B. Dörich and K. Zerulla: Wellposedness and regularity for linear Maxwell equations with surface current. Z. Angew. Math. Phys. 74, 131, 2023 Link, Preprint
- B. Dörich, J. Leibold, and B. Maier: Optimal W^{1,\infty}-estimates for an isoparametric finite element discretization of elliptic boundary value problems. Electron. Trans. Numer. Anal., 58:1--21, 2023. Link, Preprint
- B. Dörich and M. Hochbruck: Exponential integrators for quasilinear wave-type equations. SIAM J. Numer. Anal., 60(3):1472–1493, 2022. Link, Preprint
- B. Dörich and J. Leibold: Full discretization error analysis of exponential integrators for semilinear wave equations. Math. Comp., 91(336):1687–1709, 2022. Link, Preprint
- S. Buchholz, B. Dörich, and M. Hochbruck: On averaged exponential integrators for semilinear wave equations with solutions of low-regularity. SN Partial Differ. Equ. Appl., 2(2), 2021. Link, Preprint
Software
- S. Daubner, A. E. Cohen, B. Dörich, S. J. Cooper: "evoxels: A differentiable physics framework for voxel-based microstructure simulations." Preprint
Thesis
B. Dörich: "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations".
PhD thesis, Karlsruher Institut für Technologie (KIT), February 2021. Link
Current List of Courses
| Semester | Titel | Typ |
|---|---|---|
| Winter Semester 2024/25 | Matrix Theory | Proseminar |
| Winter Semester 2023/24 | Space and time discretization of nonlinear wave equations | Lecture |
| Winter Semester 2020/21 | Finite Element Methods | Lecture |
| Winter Semester 2019/20 | Functions of Matrices | Lecture |
| Summer Semester 2018 | Numerical Linear Algebra in Image Processing | Lecture |