Volume 53, Number 3, May-June 2019
|Page(s)||729 - 747|
|Published online||05 June 2019|
An easily computable error estimator in space and time for the wave equation
Laboratoire de Mathématiques de Besançon, CNRS UMR 6623, Univ. Bourgogne Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France
2 Institute of Mathematics, Ecole Polytechnique Fédérale de Lausanne, Station 8, CH 1015 Lausanne, Switzerland
* Corresponding author: firstname.lastname@example.org
Accepted: 25 August 2018
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.
Mathematics Subject Classification: 65M15 / 65M50 / 65M60
Key words: a posteriori error bounds in time and space / wave equation / Newmark scheme
© The authors. Published by EDP Sciences, SMAI 2019
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