Semigroup stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems

Coulombel, Jean-François; Gloria, Antoine

doi:10.1090/S0025-5718-10-02368-9

Semigroup stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems
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by Jean-François Coulombel and Antoine Gloria PDF

Math. Comp. 80 (2011), 165-203 Request permission

Abstract:

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

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