Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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

Juliette Chabassier 1 Sébastien Imperiale 2, 3
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [37 references]  Display  Hide  Download

https://hal.inria.fr/hal-01894357
Contributor : Sébastien Imperiale <>
Submitted on : Wednesday, October 7, 2020 - 9:03:23 AM
Last modification on : Wednesday, October 14, 2020 - 4:21:41 AM

File

LocalDiscSpaceTime.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01894357, version 3

Citation

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

Share

Metrics

Record views

38

Files downloads

53