Semi-group stability of finite difference schemes in corner domains

Antoine Benoit 1, 2
2 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
Abstract : In this article we are interested in the semi-group stability for finite difference discretizations of hyperbolic systems of equations in corner domains. We give generalizations of the results of [CG11] and [Cou15] from the half space geometry to the quarter space geometry. The most interesting fact is that the proofs of [CG11] and [Cou15] can be adaptated with minor changes to apply in the quarter space geometry. This is due to the fact that both methods in [CG11] and [Cou15] are based on energy methods and the construction of auxiliary problems with strictly dissipative boundary conditions which are known to be suitable for the strong well-posed for initial boundary value problems in the quarter space.
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Antoine Benoit. Semi-group stability of finite difference schemes in corner domains. Numerical Mathematics: Theory, Methods and Applications, Global Science Press, 2018. ⟨hal-01417105⟩

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