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Time and space adaptivity of the wave equation discretized in time by a second-order scheme

Abstract : The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. An error estimate is derived in the L∞-in-time/energy-in-space norm. Numerical experiments are reported for several test cases and confirm equivalence of the proposed estimator and the true error.
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https://hal-univ-fcomte.archives-ouvertes.fr/hal-03126851
Contributor : Alexei Lozinski <>
Submitted on : Monday, February 1, 2021 - 10:12:30 AM
Last modification on : Monday, April 26, 2021 - 11:39:55 AM

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Alexei Lozinski, Olga Gorynina, Marco Picasso. Time and space adaptivity of the wave equation discretized in time by a second-order scheme. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2019, 39 (4), pp.1672-1705. ⟨10.1093/imanum/dry048⟩. ⟨hal-03126851⟩

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