Research Group Computational PDEs
Finite element methods for flow problems and problems on moving and complex geometries — University of Göttingen.
Many physical processes are modelled by partial differential equations (PDEs), yet only rarely can these be solved analytically. We develop and analyse modern numerical methods — primarily finite element methods — that deliver reliable approximations efficiently, stably and in a structure-preserving way.
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Research
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Geometrically unfitted finite element methods
High-order accurate, robust finite element methods for PDEs on complex and moving geometries that are not resolved by the computational mesh.
Space-time finite element methods
Higher-order space-time discretizations for PDEs on moving domains — provably high-order accurate in space and time.
Free boundary problems and moving interfaces
Two-phase flows, wetting and moving fronts in biology — free boundary problems solved with unfitted and space-time finite elements.
Trefftz and embedded Trefftz DG methods
A flexible, efficient route to Trefftz discontinuous Galerkin methods that drastically reduces the cost of DG while keeping its approximation power.
Structure-preserving discretizations for flows
Pressure-robust, exactly divergence-free H(div)-conforming finite element methods for incompressible flows.
Incompressible flows on curved surfaces
Structure-preserving higher-order discretizations for incompressible viscous and inviscid flows posed on general curved surfaces.
Hybrid Discontinuous Galerkin methods
Reducing the cost of discontinuous Galerkin methods through hybridization, enabling efficient high-order and structure-preserving discretizations.
Wave propagation problems
Stable and efficient discretizations for time-harmonic wave propagation — from oscillations of the Sun to acoustics in liquid crystals.
Further topics
Further threads of the group — analog computing, reduced-order modeling, and open science / reproducible research (LiveDocs).