Semi-group stability of finite difference schemes in corner domains - Archive ouverte HAL Access content directly
Journal Articles Numerical Mathematics: Theory, Methods and Applications Year : 2018

Semi-group stability of finite difference schemes in corner domains

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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Dates and versions

hal-01417105 , version 1 (15-12-2016)

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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⟩
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