Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 618-654.
Published online: 2018-11
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017-OA-0072}, url = {http://global-sci.org/intro/article_detail/nmtma/12447.html} }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.