News & events

'100 years since Erich Trefftz's 1926 seminal paper' — Vienna, Austria.

The annual NGSolve user meeting — Zurich, Switzerland.

A nerdy card game on inf-sup stable finite element pairs for the Stokes problem.

A two-part series on embedded Trefftz DG methods for steady incompressible flow — to our knowledge the first Trefftz analysis for a genuinely nonlinear PDE, with optimal convergence rates. Part I covers the Oseen problem; Part II extends to the full nonlinear Navier-Stokes equations via a Picard fixed-point argument.

High-order surface flow discretizations via discrete Helmholtz–Hodge decompositions, by T. Brüers, C. Lehrenfeld, T. van Beeck, M. Wardetzky.

Pressure-robustness for the axisymmetric Stokes problem by velocity reconstruction, by P. L. Lederer, C. Lehrenfeld, C. Merdon, T. van Beeck.

Streamfunction-vorticity formulation for incompressible viscid and inviscid flows on general surfaces, by T. Brüers, C. Lehrenfeld, M. Wardetzky.

'On the Conforming Trefftz Finite Element Method and Applications'.

Hybrid discontinuous Galerkin discretizations for the damped time-harmonic Galbrun's equation, by M. Halla, C. Lehrenfeld, T. van Beeck.

Analysis and numerical analysis of the Helmholtz-Korteweg equation, by P. E. Farrell, T. van Beeck, U. Zerbinati.

'Higher Order Unfitted Space-Time Finite Element Methods for Moving Domain Problems'.

'Distributed memory parallel computing for Discontinuous Galerkin methods in the Finite Element Software NGSolve'.

Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions, by P. L. Lederer, C. Lehrenfeld, P. Stocker, I. Voulis.

'Space-time Trefftz DG methods for parabolic PDEs'.

An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems, by T. van Beeck, U. Zerbinati.

LiveDocs: Crafting Interactive Development Environments From Research Findings, by P. Costa Klein, C. Lehrenfeld, M. Osterhoff, M. Uecker — an Open Science contribution.

'On stable discontinuous Galerkin discretizations for Galbrun's equation'.

'Embedded Trefftz Trace DG Methods for PDEs on unfitted Surfaces'.

'High-order Unfitted Discretizations for Partial Differential Equations Coupled with Geometric Flow'.

'Spectral Deferred Correction Methods for Spatially Discretized Flow Problems'.

'Robust Finite Element Discretizations for a PDE arising in Helioseismology'.

'Monolithic Unfitted Space-Time FEM for an Osmotic Cell Swelling Problem'.

'Model Order Reduction for incompressible flows based on structure preserving discretizations'.

'Pure Eulerian unfitted FEM for Biological Fluid-Structure Interaction Problems'.

'The Virtual Element Method for Poisson's equation in two-space dimensions'.

'Learned infinite elements for helioseismology'.

'An HDG method for the Spalart-Allmaras model'.

'Boundary layer enriched Hybrid Discontinuous Galerkin Methods for Convection dominated flow'.

'On a Discontinuous Galerkin discretization for a degenerate diffusion equation'.

'On Discontinuous- and Continuous-In-Time Unfitted Space-Time Methods for PDEs on Moving Domains'.

Course on physics modeling, experiments and simulation with ODEs and PDEs for high-school students (in German), given jointly with Carsten Nowak at XLAB Göttingen.

'Higher order stabilized time stepping in unfitted finite element method on moving domains'.

'Higher order Discontinuous Galerkin methods for the Laplace-Beltrami problem on unfitted smooth surfaces'.

'Higher order unfitted isoparametric space-time FEM on moving domains'.

'Shape Optimization for Interface Problems using unfitted Finite Elements'.

'Model order reduction for linear PDE problems with the reduced basis method'.