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

Jean-François Coulombel (1) , Antoine Gloria (1)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids

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.

Mots clés: Hyperbolic systems; initial boundary value problems; finite difference schemes; stability

Domaines: Analyse numérique [math.NA]

Jean-François Coulombel, Antoine Gloria. Semigroup stability of finite difference schemes for multidimensional hyperbolic initial boundary value problems. Mathematics of Computation, 2011, 80 (273), pp.165-203. ⟨10.1090/S0025-5718-10-02368-9⟩. ⟨hal-00383891⟩