Advances in Differential Equations
- Adv. Differential Equations
- Volume 19, Number 1/2 (2014), 1-29.
Penalization for non-linear hyperbolic system
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.
Adv. Differential Equations, Volume 19, Number 1/2 (2014), 1-29.
First available in Project Euclid: 12 November 2013
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Auphan, Thomas. Penalization for non-linear hyperbolic system. Adv. Differential Equations 19 (2014), no. 1/2, 1--29. https://projecteuclid.org/euclid.ade/1384278130