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

Titel	Links	Typ
Wintersemester 2025/26
Finite Element Methods		Vorlesung (V)
Tutorial for 0110300 (Finite Element Methods)		Übung (Ü)
Sommersemester 2025
Einführung in das Wissenschaftliche Rechnen		Vorlesung (V)
Praktikum zu 0165000 (Einführung in das Wissenschaftliche Rechnen)		Praktikum (P)
Wintersemester 2024/25
Seminar (Spezielle Themen der Numerik)		Seminar (S)

Publikationsliste

2025

Approximation of minimizers of the Ginzburg–Landau energy in non-convex domains
Dörich, B.
2025. KIT, Karlsruhe. doi:10.5445/IR/1000183843

Gautschi-type and implicit-explicit integrators for constrained wave equations
Altmann, R.; Dörich, B.; Zimmer, C.
2025. KIT, Karlsruhe

Strong Norm Error Bounds for Quasilinear Wave Equations Under Weak CFL-Type Conditions
Dörich, B.
2025. Foundations of Computational Mathematics, 25 (1), 303–350. doi:10.1007/s10208-024-09639-w

Finite element discretization of nonlinear models of ultrasound heating
Careaga, J.; Dörich, B.; Nikolić, V.
2025. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000178566

2024

A multiscale approach to the stationary Ginzburg–Landau equations of superconductivity
Döding, C.; Dörich, B.; Henning, P.
2024. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000174322

Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions
Dörich, B.; Dörner, J.; Hochbruck, M.
2024. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000173144

Maximum norm error bounds for the full discretization of nonautonomous wave equations
Dörich, B.; Leibold, J.; Maier, B.
2024. IMA Journal of Numerical Analysis, 44 (4), 2480–2512. doi:10.1093/imanum/drad065

Variational Gaussian approximation for the magnetic Schrödinger equation *
Burkhard, S.; Dörich, B.; Hochbruck, M.; Lasser, C.
2024. Journal of Physics A: Mathematical and Theoretical, 57 (29), 295202. doi:10.1088/1751-8121/ad591e

Error Bounds for Discrete Minimizers of the Ginzburg–Landau Energy in the High- Regime
Dörich, B.; Henning, P.
2024. SIAM Journal on Numerical Analysis, 62 (3), 1313–1343. doi:10.1137/23M1560938

Robust fully discrete error bounds for the Kuznetsov equations in the inviscid limit
Dörich, B.; Nikolić, V.
2024. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000167217

2023

Variational Gaussian approximation for the magnetic Schrödinger equation
Burkhard, S.; Dörich, B.; Hochbruck, M.; Lasser, C.
2023. arxiv. doi:10.48550/arXiv.2310.16734

Variational Gaussian approximation for the magnetic Schrödinger equation
Burkhard, S.; Dörich, B.; Hochbruck, M.; Lasser, C.
2023. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000154431/v2

Wellposedness and regularity for linear Maxwell equations with surface current
Dörich, B.; Zerulla, K.
2023. Zeitschrift für angewandte Mathematik und Physik, 74 (4), Art.-Nr.: 131. doi:10.1007/s00033-023-02021-w

Error bounds for discrete minimizers of the {G}inzburg--{L}andau energy in the high- regime
Dörich, B.; Henning, P.
2023. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000156898

Optimal -estimates for an isoparametric finite element discretization of elliptic boundary value problems
Dörich, B.; Leibold, J.; Maier, B.
2023. ETNA - Electronic Transactions on Numerical Analysis, 58, 1–21. doi:10.1553/etna_vol58s1

2022

Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions
Dörich, B.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000151366

Wellposedness and regularity for linear Maxwell equations with surface current
Dörich, B.; Zerulla, K.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000148883

Full discretization error analysis of exponential integrators for semilinear wave equations
Dörich, B.; Leibold, J.
2022. Mathematics of Computation, 91 (336), 1687–1709. doi:10.1090/MCOM/3736

Exponential Integrators for Quasilinear Wave-Type Equations
Dörich, B.; Hochbruck, M.
2022. SIAM Journal on Numerical Analysis, 60 (3), 1472–1493. doi:10.1137/21M1410579

Optimal W-estimates for an isoparametric finite element discretization of elliptic boundary value problems
Dörich, B.; Leibold, J.; Maier, B.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000142881/v2

2021

Maximum norm error bounds for the full discretization of non-autonomous wave equations
Dörich, B.; Leibold, J.; Maier, B.
2021. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000141540

Stability and convergence of the Ritz map in the maximum norm for nonconforming finite elements
Dörich, B.; Leibold, J.; Maier, B.
2021. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000141502/v2

Full discretization error analysis of exponential integrators for semilinear wave equations
Dörich, B.; Leibold, J.
2021. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000135100

On averaged exponential integrators for semilinear wave equations with solutions of low-regularity
Buchholz, S.; Dörich, B.; Hochbruck, M.
2021. SN Partial Differential Equations and Applications, 2 (2), Art.-Nr.: 23. doi:10.1007/s42985-020-00045-9

Exponential integrators for quasilinear wave-type equations
Dörich, B.; Hochbruck, M.
2021. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000131210

2020

On averaged exponential integrators for semilinear wave equations with solutions of low-regularity
Buchholz, S.; Dörich, B.; Hochbruck, M.
2020. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000117802