34 citations · 86 across the 10 of their papers we have counts for
11 papers
On the limiting amplitude principle for the wave equation with variable coefficients
Anton Arnold, Sjoerd Geevers, Ilaria Perugia +1
In this paper, we prove new results on the validity of the limiting amplitude principle (LAP) for the wave equation with nonconstant coefficients, not necessarily in divergence for…
On the exponential time-decay for the one-dimensional wave equation with variable coefficients
Anton Arnold, Sjoerd Geevers, Ilaria Perugia +1
We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded r…
Fast mass lumped multiscale wave propagation modelling
Sjoerd Geevers, Roland Maier
In this paper, we investigate the use of a mass lumped fully explicit time stepping scheme for the discretisation of the wave equation with underlying material parameters that vary…
An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients
Anton Arnold, Sjoerd Geevers, Ilaria Perugia +1
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities.…
A polynomial-degree-robust a posteriori error estimator for Nédélec discretizations of magnetostatic problems
Joscha Gedicke, Sjoerd Geevers, Ilaria Perugia +1
We present an equilibration-based a posteriori error estimator for Nédélec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient corr…
An equilibrated a posteriori error estimator for arbitrary-order Nédélec elements for magnetostatic problems
Joscha Gedicke, Sjoerd Geevers, Ilaria Perugia
We present a novel \textit{a posteriori} error estimator for Nédélec elements for magnetostatic problems that is constant-free, i.e. it provides an upper bound on the error that do…
Efficient quadrature rules for computing the stiffness matrices of mass-lumped tetrahedral elements for linear wave problems
S. Geevers, W. A. Mulder, J. J. W. van der Vegt
We present new and efficient quadrature rules for computing the stiffness matrices of mass-lumped tetrahedral elements for wave propagation modelling. These quadrature rules allow…
Doubling the convergence rate by pre- and post-processing the finite element approximation for linear wave problems
Sjoerd Geevers
In this paper, a novel pre- and post-processing algorithm is presented that can double the convergence rate of finite element approximations for linear wave problems. In particular…
New Higher-Order Mass-Lumped Tetrahedral Elements for Wave Propagation Modelling
S. Geevers, W. A. Mulder, J. J. W. van der Vegt
We present a new accuracy condition for the construction of continuous mass-lumped elements. This condition is less restrictive than the one currently used and enabled us to constr…
Dispersion Properties of Explicit Finite Element Methods for Wave Propagation Modelling on Tetrahedral Meshes
S. Geevers, W. A. Mulder, J. J. W. van der Vegt
We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped f…
Sharp Penalty Term and Time Step Bounds for the Interior Penalty Discontinuous Galerkin Method for Linear Hyperbolic Problems
S. Geevers, J. J. W. van der Vegt
We present sharp and sufficient bounds for the interior penalty term and time step size to ensure stability of the Symmetric Interior Penalty Discontinuous Galerkin (SIPDG) method…