8 papers
An Aubin-Nitsche Lemma for a positivity-preserving finite element method
Gabriel R. Barrenechea, Theophile Chaumont-Frelet
In this work we prove an Aubin-Nitsche Lemma for a positivity-preserving discretisation of an elliptic problem. Due to the nonlinearity of the discretisation, the result requires a…
Spectral coarse spaces based on indefinite operators: the -GenEO method
Théophile Chaumont-Frelet, Victorita Dolean, Mark Fry +2
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method for constructing coarse spaces used in the preconditioning of iterative solvers for discrete PDEs. This method…
Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality
T. Chaumont-Frelet
We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower b…
Optimal convergence rates of an adaptive finite element method for unbounded domains
Théophile Chaumont-Frelet, Gregor Gantner
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessa…
A generalized Hessian-based error estimator for an IPDG formulation of the biharmonic problem in two dimensions
Théophile Chaumont-Frelet, Joscha Gedicke, Lorenzo Mascotto
We consider a two dimensional biharmonic problem and its discretization by means of a symmetric interior penalty discontinuous Galerkin method. A novel split of an error measure ba…
Duality analysis of interior penalty discontinuous Galerkin methods under minimal regularity and application to the a priori and a posteriori error analysis of Helmholtz problems
T. Chaumont-Frelet
We consider interior penalty discontinuous Galerkin discretizations of time-harmonic wave propagation problems modeled by the Helmholtz equation, and derive novel a priori and a po…
Efficient approximation of high-frequency Helmholtz solutions by Gaussian coherent states
T. Chaumont-Frelet, V. Dolean, M. Ingremeau
We introduce new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients in dimension $d…
A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem
T. Chaumont-Frelet
We introduce two a posteriori error estimators for Nédélec finite element discretizations of the curl-curl problem. These estimators pertain to a new Prager-Synge identity and an a…