Staff Dr. Christian Döding

Address:
Institut für Numerische Simulation
Friedrich-Hirzebruch-Allee 7
53115 Bonn
Phone: +49 228 73-69745
Office: FHA7 1.039
E-Mail: ed tod nnob-inu tod sni ta gnideoda tod b@foo tod de

Research interest

My research interest includes the numerical analysis of partial differential equations and applied dynamical systems. In particular, I am interested in:

Numerical methods for partial differential equations

  • (multiscale) finite element methods
  • structure-preserving time integration
  • nonlinear minimization problems
  • convergence analysis and a-priori error estimates
  • nonlinear Schrödinger equations, Gross-Pitaevskii equations, Ginzburg-Landau equations
  • application to quantum physics: Bose-Einstein condensates and superconductivity

Analysis of nonlinear waves in evolution equations

  • dynamics of patterns
  • stability, existence and numerical computation of nonlinear waves

Short CV

  • since 2023: Postdoc at University of Bonn, Institute for Numerical Simulation
  • 2021-2023: Postdoc at Ruhr University Bochum, Department of Mathematics
  • 2019-2021: Nonacademic Employment at Syskoplan Reply GmbH
  • 2019: Doctorate at Bielefeld University, Supervisor: Wolf-Jürgen Beyn
  • 2015-2019: PhD-student, Bielefeld University
  • 2013-2015: Study of Mathematics (M.Sc.), Bielefeld University
  • 2013-2015: Student Assistant, Bielefeld University, SFB 701
  • 2010-2013: Study of Mathematics and Physics (B.Sc.), Bielefeld University

Publications

Preprints

  1. Algebraic rates of stability for front-type modulated waves in Ginzburg Landau equations. W.-J. Beyn and C. Döding. preprint, 2024. BibTeX arXiv
  2. A multiscale approach to the stationary Ginzburg-Landau equations of superconductivity. C. Döding, B. Dörich, and P. Henning. preprint, 2024. BibTeX arXiv

Articles

  1. Vortex-capturing multiscale spaces for the Ginzburg-Landau equation. M. Blum, C. Döding, and P. Henning. Multiscale Model. Simul., 2024+ (to appear). BibTeX arXiv
  2. Localized orthogonal decomposition methods vs. classical FEM for the Gross-Pitaevskii equation. C. Döding. In Numerical mathematics and advanced applications (ENUMATH 2023), Lect. Notes Comput. Sci. Eng. 2024+ (to appear). BibTeX arXiv
  3. A two level approach for simulating Bose-Einstein condensates by localized orthogonal decomposition. C. Döding, P. Henning, and J. Wärnegård. ESAIM Math. Model. Numer. Anal., 58(6):2317–2349, 2024. BibTeX DOI arXiv
  4. Uniform L∞L^\infty -bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation. C. Döding and P. Henning. IMA J. Numer. Anal., 44(5):2892–2935, 2023. BibTeX DOI arXiv
  5. Stability of traveling oscillating fronts in complex Ginzburg Landau equations. W.-J. Beyn and C. Döding. SIAM J. Math. Anal., 54(5):5447–5488, 2022. BibTeX DOI arXiv

Thesis

  1. Stability of traveling oscillating fronts in parabolic evolution equations. C. Döding. PhD Thesis, Department of Mathematics, Bielefeld University, 2019. BibTeX DOI
  2. Numerische Lösung parabolischer Gleichungen mit quadraturbasierten Integratoren. C. Döding. Master Thesis, Department of Mathematics, Bielefeld University, 2015. BibTeX pdf