An easily computable error estimator in space and time for the wave equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 3, pp. 729-747.

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.

DOI : 10.1051/m2an/2018049
Classification : 65M15, 65M50, 65M60
Mots-clés : a posteriori error bounds in time and space, wave equation, Newmark scheme
Gorynina, O. 1 ; Lozinski, A. 1 ; Picasso, M. 1

1 
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     title = {An easily computable error estimator in space and time for the wave equation},
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Gorynina, O.; Lozinski, A.; Picasso, M. An easily computable error estimator in space and time for the wave equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 3, pp. 729-747. doi : 10.1051/m2an/2018049. http://www.numdam.org/articles/10.1051/m2an/2018049/

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