4 papers
A hybrid -interior penalty method for the nematic Helmholtz--Korteweg equation
Tim van Beeck
The nematic Helmholtz--Korteweg equation models the propagation of time-harmonic acoustic waves in nematic Korteweg fluids, such as nematic liquid crystals. The PDE augments the cl…
Releasing the pressure: High-order surface flow discretizations via discrete Helmholtz-Hodge decompositions
Tim Brüers, Christoph Lehrenfeld, Tim van Beeck +1
We present a discrete Helmholtz--Hodge decomposition for H(div)-conforming Brezzi--Douglas--Marini (BDM) finite elements on triangulated surfaces of arbitrary topology. The diverge…
Variational data assimilation for the wave equation in heterogeneous media: Numerical investigation of stability
Erik Burman, Janosch Preuss, Tim van Beeck
In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the…
An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems
Tim van Beeck, Umberto Zerbinati
It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, di…