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Staff Dr. Christian Döding

Contact Information

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

  • M. Blum, C. Döding and P. Henning: Vortex-capturing multiscale spaces for the Ginzburg-Landau equation, 2024, preprint
  • W.-J. Beyn and C. Döding: Algebraic rates of stability for front-type modulated waves in Ginzburg Landau equations, 2024, preprint
  • C. Döding: Localized Orthogonal Decomposition Methods vs. Classical FEM for the Gross-Pitaevskii Equation, 2024, preprint

Articles

  • C. Döding, P. Henning and J. Wärnegård: A two level approach for simulating Bose-Einstein condensates by localized orthogonal decomposition, to appear in ESAIM Math. Model. Numer. Anal., 2024, DOI, preprint
  • C. Döding and P. Henning: Uniform L∞-bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation, to appear in IMA J. Numer. Anal., 2023, DOI, preprint
  • W.J. Beyn and C. Döding: Stability of Traveling Oscillating Fronts in Complex Ginzburg Landau Equations, SIAM J. Math. Anal., 54(5):5447–5488, 2022, DOI, preprint

Thesis

  • C. Döding: Stability of traveling oscillating fronts in parabolic evolution equations, Phd-thesis, Department of Mathematics, Bielefeld University, 2019, DOI
  • C. Döding: Numerische Lösung parabolischer Gleichungen mit quadraturbasierten Integratoren, Master thesis, Department of Mathematics, Bielefeld University, 2015, PDF