Volume 11, Issue 3
Semi-Group Stability of Finite Difference Schemes in Corner Domains

Antoine Benoit

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 618-654.

Published online: 2018-11

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  • Abstract

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.

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@Article{NMTMA-11-618, author = {}, title = {Semi-Group Stability of Finite Difference Schemes in Corner Domains}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {3}, pages = {618--654}, abstract = {

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} }
TY - JOUR T1 - Semi-Group Stability of Finite Difference Schemes in Corner Domains 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.

Antoine Benoit. (2020). Semi-Group Stability of Finite Difference Schemes in Corner Domains. Numerical Mathematics: Theory, Methods and Applications. 11 (3). 618-654. doi:10.4208/nmtma.2017-OA-0072
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