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Preprints, Working Papers, ... Year : 2020

Construction and convergence analysis of conservative second order local time discretisation for linear wave equations

Abstract

In this work we present and analyse a time discretisation strategy for linear wave equations that 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 numerical illustrations that confirm the obtained theoretical results and we compare our approach to other existing local time stepping strategies for wave equations.
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Dates and versions

hal-01894357 , version 1 (12-10-2018)
hal-01894357 , version 2 (30-08-2019)
hal-01894357 , version 3 (07-10-2020)

Identifiers

  • HAL Id : hal-01894357 , version 3

Cite

Juliette Chabassier, Sébastien Imperiale. Construction and convergence analysis of conservative second order local time discretisation for linear wave equations. 2020. ⟨hal-01894357v3⟩
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