Tim van Beeck
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View article: Variational data assimilation for the wave equation in heterogeneous media: Numerical investigation of stability
Variational data assimilation for the wave equation in heterogeneous media: Numerical investigation of stability Open
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 space-time cylinder have been proposed. This problem enjoys…
Hybrid discontinuous Galerkin discretizations for the damped time-harmonic Galbrun's equation Open
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 discretizations (HDG) that are stable and optimally convergent for al…
View article: Analysis and numerical analysis of the Helmholtz-Korteweg equation
Analysis and numerical analysis of the Helmholtz-Korteweg equation Open
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 of nematic order. A prominent example is given by nematic l…
Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem Open
In this paper we present a new -conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is to for…
An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems Open
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, different criteria have been proposed to ensure uniform quasi…
Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem Open
In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is …