An easily computable error estimator in space and time for the wave equation

Olga Gorynina (1, 2) , Alexei Lozinski (3) , Marco Picasso (4)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS
3 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
4 EPFL - Ecole Polytechnique Fédérale de Lausanne

We propose a cheaper version of a posteriori error estimator from Gorynina et al. (Numer. Anal. (2017)) for the linear second-order wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator preserves all the properties of the previous one (reliability, optimality on smooth solutions and quasi-uniform meshes) but no longer requires an extra computation of the Laplacian of the discrete solution on each time step.

Mots clés: A posteriori error bounds in time and space; Wave equation; Newmark scheme

Domaines: Mathématiques [math]

Olga Gorynina, Alexei Lozinski, Marco Picasso. An easily computable error estimator in space and time for the wave equation. ESAIM: Mathematical Modelling and Numerical Analysis, 2019, 53 (3), pp.729-747. ⟨10.1051/m2an/2018049⟩. ⟨hal-02922758⟩