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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

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. B. Dörich and P. Henning: Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-$\kappa$ regime. Preprint
  2. S. Burkhard, B. Dörich, M. Hochbruck, and C. Lasser: Variational Gaussian approximation for the magnetic Schrödinger equation. Preprint
  3. B. Dörich: Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions. Preprint
  4. B. Dörich and K. Zerulla: Wellposedness and regularity for linear Maxwell equations with surface current. Preprint
  5. B. Dörich, J. Leibold, and B. Maier: Maximum norm error bounds for the full discretization of non-autonomous wave equations. Preprint

Publications

  1. 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
  2. B. Dörich and M. Hochbruck: Exponential integrators for quasilinear wave-type equations. SIAM J. Numer. Anal., 60(3):1472–1493, 2022. Link, Preprint
  3. 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
  4. 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
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