Semi-group stability of finite difference schemes in corner domains

Antoine Benoit (1, 2)

1 ULB - Département de Mathématique [Bruxelles]
2 MEPHYSTO - Quantitative methods for stochastic models in physics

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.

Domaines: Analyse numérique [math.NA]

Antoine Benoit. Semi-group stability of finite difference schemes in corner domains. Numerical Mathematics: Theory, Methods and Applications, 2018, 11 (3), pp.618-654. ⟨10.4208/nmtma.2017-OA-0072⟩. ⟨hal-01417105⟩