5 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…
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…
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…