Department of Mathematics
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Institute for Applied and Numerical Mathematics
Research Group 1: Numerical Analysis
Dr. Benjamin Dörich
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Dr. Benjamin Dörich

  • Englerstr. 2
    76131 Karlsruhe

Link to my Junior Research Group Numerical methods for nonlinear optics.

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

  1. C. Döding, B. Dörich, and P. Henning: A multiscale approach to the stationary Ginzburg–Landau equations of superconductivity Preprint
  2. B. Dörich, J. Dörner, and M. Hochbruck: Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions Preprint
  3. B. Dörich and V. Nikolić: Robust fully discrete error bounds for the Kuznetsov equations in the inviscid limit. Preprint

Publications

  1. 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
  2. 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
  3. B. Dörich: Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions. Found. Comput. Math. Link, Preprint
  4. 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
  5. B. Dörich and K. Zerulla: Wellposedness and regularity for linear Maxwell equations with surface current. Z. Angew. Math. Phys. 74, 131, 2023 Link, Preprint
  6. 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
  7. B. Dörich and M. Hochbruck: Exponential integrators for quasilinear wave-type equations. SIAM J. Numer. Anal., 60(3):1472–1493, 2022. Link, Preprint
  8. 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
  9. 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

Current List of Courses
Semester Titel Typ
Winter Semester 2024/25 Seminar (Spezielle Themen der Numerik) Seminar
Matrix Theory Proseminar
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
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