A general equivalence theorem in the theory of discretization methods

Sanz-Serna, J. M.; Palencia, C.

doi:10.1090/S0025-5718-1985-0790648-7

A general equivalence theorem in the theory of discretization methods
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by J. M. Sanz-Serna and C. Palencia PDF

Math. Comp. 45 (1985), 143-152 Request permission

Abstract:

The Lax-Richtmyer theorem is extended to work in the framework of Stetter’s theory of discretizations. The new result applies to both initial and boundary value problems discretized by finite elements, finite differences, etc. Several examples are given, together with a comparison with other available equivalence theorems. The proof relies on a generalized Banach-Steinhaus theorem.

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