Semigroup stability of finite difference schemes for multidimensional hyperbolic initial boundary value problemsReport as inadecuate




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1 SIMPAF - SImulations and Modeling for PArticles and Fluids LPP - Laboratoire Paul Painlevé, Inria Lille - Nord Europe 2 LPP - Laboratoire Paul Painlevé

Abstract : We develop a simple energy method to prove the stability of finite difference schemes for multidimensional hyperbolic initial boundary value problems. In particular we extend to several space dimensions a crucial result by Goldberg and Tadmor. This allows us to give two conditions on the discretized operator that ensure that stability estimates for zero initial data imply a semigroup stability estimate for general initial data. We then apply this criterion to several numerical schemes in two space dimensions.

Keywords : finite difference schemes stability Hyperbolic systems initial boundary value problems





Author: Jean-François Coulombel - Antoine Gloria -

Source: https://hal.archives-ouvertes.fr/



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