Tim van Beeck

I am a PhD student supervised by Christoph Lehrenfeld and a member of the CRC 1456. My research is currently focussed the development and analysis of numerical methods for Galbrun's equation, a PDE that models the propagation of waves in the sun. I also work on the numerical analysis of the nematic Helmholtz--Korteweg equation, which models the propagation of acoustic waves in nematic liquid crystals. Previously, I wrote my Master's thesis on discontinuous Galerkin discretizations for Galbrun's equation and my Bachelor’s Thesis on a DG discretization for a degenerate diffusion equation in the working group. I have also contributed to a project on unfitted mixed finite element methods.

Publications

• T. Brüers, C. Lehrenfeld, TvB, M. Wardetzky, "Releasing the pressure: High-order surface flow discretizations via discrete Helmholtz--Hodge decompositions", arXiv preprint, arXiv:2603.27714, (2026), PDF.
• P. L. Lederer, C. Lehrenfeld, C. Merdon, TvB, "Pressure-robustness for the axisymmetric Stokes problem by velocity reconstruction", arXiv preprint, arXiv:2603.01030, (2026), PDF.
• E. Burman, J. Preuß, TvB, "Variational data assimilation for the wave equation in heterogeneous media", arXiv preprint, arXiv:2509.13108, (2025), PDF.
• M. Halla, C. Lehrenfeld, TvB, "Hybrid discontinuous Galerkin discretizations for the damped time-harmonic Galbrun's equation", arXiv preprint, arXiv:2504.09547, (2025), PDF.
• P. E. Farrell, TvB, U. Zerbinati, "Analysis and numerical analysis of the Helmholtz-Korteweg equation", arXiv preprint, arXiv:2503.10771, (2025), PDF.
• TvB, U. Zerbinati, "An adaptive mesh refinement strategy to ensure quasi-optimality of the conforming finite element method for the Helmholtz equation via T-coercivity", arXiv preprint, arXiv:2403.06266, (2024), PDF.
• C. Lehrenfeld, TvB, I. Voulis, "Analysis of divergence-preserving unfitted mixed finite element methods for the mixed Poisson problem.", Math. Comp., (2025), Preprint.

Theses

• TvB (2023): "On stable discontinuous Galerkin discretizations for Galbrun's equation.", Master's thesis, NAM, University of Göttingen, http.
• TvB (2021): "On a Discontinuous Galerkin discretization for a degenerate diffusion equation.", Bachelor's thesis, NAM, University of Göttingen, http.

Travel

Research visits

• March 02-09, 2026, University of Oxford, UK, with Patrick E. Farrell and Umberto Zerbinati
• October 13-20, 2025, University of Oxford, UK, with Umberto Zerbinati
• December 09-16, 2024: Pavia, Italy, with Umberto Zerbinati
• January-March 2024: UCL London, UK, with Erik Burman and Janosch Preuß

Conferences and workshops

• Special Topic School: "Optimality of adaptive finite element methods", Bonn, Germany
• ENUMATH 2025, Heidelberg, Germany
• NGSolve Usermeeting 2025, Hamburg, Germany
• EFEF 2025, Trieste, Italy
• Conference on Mathematics of Wave Phenomena 2025, Karlsruhe, Germany
• GAMM Numerical Analysis 2024, Augsburg, Germany
• GAMM ANLA 2024, Göttingen, Germany
• CRC 1456 Retreat 2024, Hofgeismar, Germany
• Chemnitz FEM Symposium 2024, Chemnitz, Germany
• WCCM 2024, Vancouver, Canada
• WAVES 2024, Berlin, Germany
• EFEF 2024, London, UK
• NGSolve Usermeeting 2024, Vienna, Austria
• NGSolve Usermeeting 2023, Portland, USA
• EFEF 2023, Enschede, Netherlands
• NoKo 2022, Hanover, Germany