7 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…
Pressure-robustness for the axisymmetric Stokes problem by velocity reconstruction
Philip L. Lederer, Christoph Lehrenfeld, Christian Merdon +1
This paper studies pressure-robustness for the axisymmetric Stokes problem. The transformation to cylindrical coordinates requires that the radially weighted velocity is divergence…
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…
Analysis and numerical analysis of the Helmholtz-Korteweg equation
Patrick E. Farrell, Tim van Beeck, Umberto Zerbinati
We analyse the nematic Helmholtz-Korteweg equation, a variant of the classical Helmholtz equation that describes time-harmonic wave propagation in calamitic fluids in the presence…
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…
Hybrid discontinuous Galerkin discretizations for the damped time-harmonic Galbrun's equation
Martin Halla, Christoph Lehrenfeld, Tim van Beeck
In this article, we study the damped time-harmonic Galbrun's equation which models solar and stellar oscillations. We introduce and analyze hybrid discontinuous Galerkin discretiza…