Volume 55, Number 4, July-August 2021
|Page(s)||1507 - 1543|
|Published online||29 July 2021|
Construction and convergence analysis of conservative second order local time discretisation for linear wave equations
Team Magique 3D, Inria, E2S UPPA, CNRS, 200 avenue de la vieille tour, 33405 Talence Cedex or avenue de l’université, 64013 Pau Cedex, France
2 Inria – LMS, École Polytechnique, CNRS – Institut Polytechnique de Paris, 1 rue Honoré d’Estienne d’Orves, 91120 Palaiseau, France
* Corresponding author: firstname.lastname@example.org
Accepted: 29 June 2021
In this work we present and analyse a time discretisation strategy for linear wave equations t hat aims at using locally in space the most adapted time discretisation among a family of implicit or explicit centered second order schemes. The proposed family of schemes is adapted to domain decomposition methods such as the mortar element method. They correspond in that case to local implicit schemes and to local time stepping. We show that, if some regularity properties of the solution are satisfied and if the time step verifies a stability condition, then the family of proposed time discretisations provides, in a strong norm, second order space-time convergence. Finally, we provide 1D and 2D numerical illustrations that confirm the obtained theoretical results and we compare our approach on 1D test cases to other existing local time stepping strategies for wave equations.
Mathematics Subject Classification: 35L05 / 65M12 / 65M22 / 65M60
Key words: Wave equations / time discretisation / converge analysis / local implicit scheme / local time stepping
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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