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arXiv · 2009.11657

The Leray-G{\aa}rding method for finite difference schemes. II. Smooth crossing modes

Jean-François Coulombel
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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].

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Jean-François Coulombel. 2020-09-23. The Leray-G{\aa}rding method for finite difference schemes. II. Smooth crossing modes. https://arxiv.org/abs/2009.11657

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