Advances in Differential Equations

Penalization for non-linear hyperbolic system

Thomas Auphan

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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.

Article information

Adv. Differential Equations, Volume 19, Number 1/2 (2014), 1-29.

First available in Project Euclid: 12 November 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L60: Nonlinear first-order hyperbolic equations 65N85: Fictitious domain methods


Auphan, Thomas. Penalization for non-linear hyperbolic system. Adv. Differential Equations 19 (2014), no. 1/2, 1--29.

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