The Leray-G{\aa}rding method for finite difference schemes. II. Smooth crossing modes
Abstract
In [Cou15] a multiplier technique, going back to Leray and G{\aa}rding for scalar hyperbolic partial differential equations, has been extended to the context of finite difference schemes for evolutionary problems. The key point of the analysis in [Cou15] was to obtain a discrete energy-dissipation balance law when the initial difference operator is multiplied by a suitable quantity. The construction of the energy and dissipation functionals was achieved in [Cou15] under the assumption that all modes were separated. We relax this assumption here and construct, for the same multiplier as in [Cou15], the energy and dissipation functionals when some modes cross. Semigroup estimates for fully discrete hy-perbolic initial boundary value problems are deduced in this broader context by following the arguments of [Cou15].
Keywords
Cite
@article{arxiv.2009.11657,
title = {The Leray-G{\aa}rding method for finite difference schemes. II. Smooth crossing modes},
author = {Jean-François Coulombel},
journal= {arXiv preprint arXiv:2009.11657},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1505.06060