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

Penalization for non-linear hyperbolic system