Towards Accurate Artificial Boundary Conditions for Nonlinear PDEs Through Examples

Xavier Antoine (1, 2) , Christophe Besse (3, 4) , Jeremie Szeftel (5)

1 EDP - Equations aux dérivées partielles
2 CORIDA - Robust control of infinite dimensional systems and applications
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 SIMPAF - SImulations and Modeling for PArticles and Fluids
5 DMA - Département de Mathématiques et Applications - ENS Paris

The aim of this paper is to give a comprehensive review of current developments related to the derivation of artificial boundary conditions for nonlinear partial differential equations. The essential tools to build such boundary conditions are based on pseudodifferential and paradifferential calculus. We present various derivations and compare them. Some numerical results illustrate their respective accuracy and analyze the potential of each technique.

Domaines: Analyse numérique [math.NA]; Mathématiques générales [math.GM]

Xavier Antoine, Christophe Besse, Jeremie Szeftel. Towards Accurate Artificial Boundary Conditions for Nonlinear PDEs Through Examples. Cubo, a Mathematical Journal, 2009, 11 (4), pp.1008-1033. ⟨hal-00755572⟩