TY - JOUR T1 - Semi-Group Stability of Finite Difference Schemes in Corner Domains AU - Antoine Benoit JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 618 EP - 654 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.2017-OA-0072 UR - https://global-sci.org/intro/article_detail/nmtma/12447.html KW - AB -

In this article we are interested in the semi-group stability for finite difference schemes approximations of hyperbolic systems of equations in corner domains. We give generalizations of the results of [10] and [9] from the half space geometry to the quarter space geometry. The most interesting fact is that the proofs of [10] and [9] can be adaptated with minor changes to apply in the quarter space geometry. This is due to the fact that both methods in [10] and [9] 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.