Penalization for non-linear hyperbolic system

Thomas Auphan (1)

1 I2M - Institut de Mathématiques de Marseille

This paper proposes a volumetric penalty method to simulate the boundary conditions for a non-linear hyperbolic problem. The boundary conditions are assumed to be maximally strictly dissipative on a non-characteristic boundary. This penalization appears to be quite natural since, after a natural change of variable, the penalty matrix is an orthogonal projector. We prove the convergence towards the solution of the wished hyperbolic problem and that this convergence is sharp in the sense that it does not generate any boundary layer, at any order. The proof involves an approximation by asymptotic expansion and energy estimates in anisotropic Sobolev spaces.

Mots clés: penalization method; hyperbolic system; energy estimates

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Thomas Auphan. Penalization for non-linear hyperbolic system. Advances in Differential Equations, 2014, 19 (1/2), pp.1-29. ⟨hal-00920129⟩