
Dr. Benjamin Dörich
-
by appointment
-
Kollegiengebäude Mathematik (20.30)
3.057
+49 721 608 46680
+49 721 608 43767
-
benjamin.doerich@kit.edu
-
Englerstr. 2
76131 Karlsruhe
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 and P. Henning: Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-$\kappa$ regime. Preprint
- S. Burkhard, B. Dörich, M. Hochbruck, and C. Lasser: Variational Gaussian approximation for the magnetic Schrödinger equation. Preprint
- B. Dörich: Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions. Preprint
Publications
- B. Dörich, J. Leibold, and B. Maier: Maximum norm error bounds for the full discretization of non-autonomous wave equations. (accepted in IMA J. Numer. Anal.) 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
Thesis
B. Dörich: "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations".
PhD thesis, Karlsruher Institut für Technologie (KIT), February 2021. Link
Semester | Titel | Typ |
---|---|---|
Winter Semester 2023/24 | Space and time discretization of nonlinear wave equations | Lecture |
Summer Semester 2023 | Numerical Methods for Time-Dependent Partial Differential Equations | Lecture |
Summer Semester 2022 | Seminar (numerische Methoden für retardierte Differentialgleichungen) | Seminar |
Winter Semester 2021/22 | Exponential Integrators | Lecture |
Summer Semester 2021 | Topics in Numerical Linear Algebra | 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 |