9 papers · 1 filter
A HDG method with transmission variables for time-harmonic wave propagation problems with constant coefficients
Simone Pescuma, Gwénaël Gabard, Théophile Chaumont-Frelet +1
Iterative finite element solvers for time-harmonic wave problems are notoriously slow to converge, owing to fundamental properties of these problems. We present a variant of the hy…
A posteriori error estimates and space-adaptive mesh refinements for time-dependent scattering problems
Théophile Chaumont-Frelet, Heiko Gimperlein, Ignacio Labarca-Figueroa +1
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a s…
A quasi-interpolation operator yielding fully computable error bounds
T. Chaumont-Frelet, M. Vohralik
We design a quasi-interpolation operator from the Sobolev space to its finite-dimensional finite element subspace formed by piecewise polynomials on a simplicial mesh wi…
A posteriori error estimates for the finite element discretization of second-order PDEs set in unbounded domains
T. Chaumont-Frelet
We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discreti…
Adaptive boundary element methods for regularized combined field integral equations
Théophile Chaumont-Frelet, Gregor Gantner
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber…
A priori and a posteriori analysis of the discontinuous Galerkin approximation of the time-harmonic Maxwell's equations under minimal regularity assumptions
T. Chaumont-Frelet, A. Ern
We derive a priori and a posteriori error estimates for the discontinuous Galerkin (dG) approximation of the time-harmonic Maxwell's equations. Specifically, we consider an interio…