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

Dr. Benjamin Dörich

  • 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

  1. R. Altmann, B. Dörich, and C. Zimmer: Gautschi-type and implicit--explicit integrators for constrained wave equations. Preprint
  2. J. Careaga, B. Dörich, and V. Nikolić: Finite element discretization of nonlinear models of ultrasound heating. Preprint
  3. C. Döding, B. Dörich, and P. Henning: A multiscale approach to the stationary Ginzburg–Landau equations of superconductivity Preprint
  4. B. Dörich, J. Dörner, and M. Hochbruck: Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions Preprint
  5. 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., 25:303–350, 2025. 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 Links Typ
Sommersemester 2025 Einführung in das Wissenschaftliche Rechnen Vorlesung (V)
Praktikum zu 0165000 (Einführung in das Wissenschaftliche Rechnen) Praktikum (P)
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