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The Leray-Gårding method for finite difference schemes. (La méthode de Leray et Gårding pour les schémas aux différences finies.) (English. French summary) Zbl 1328.65175
Summary: In the fifties, Leray and Gårding have developed a multiplier technique for deriving a priori estimates for solutions to scalar hyperbolic equations. The existence of such a multiplier is the starting point of the argument by J. Rauch [Commun. Pure Appl. Math. 25, 265–285 (1972; Zbl 0226.35056)] for the derivation of semigroup estimates for hyperbolic initial boundary value problems. In this article, we explain how this multiplier technique can be adapted to the framework of finite difference approximations of transport equations. The technique applies to numerical schemes with arbitrarily many time levels. The existence and properties of the multiplier enable us to derive optimal semigroup estimates for fully discrete hyperbolic initial boundary value problems.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L03 Initial value problems for first-order hyperbolic equations
35L04 Initial-boundary value problems for first-order hyperbolic equations
Software:
Eigtool; RODAS
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