A general equivalence theorem in the theory of discretization methods. (English) Zbl 0599.65034

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

Math. Comput. 45, 143-152 (1985).

For initial and boundary value problems discretized by finite differences, by finite elements, etc. the Lax-Richtmyer theorem is generalized. Several examples are given.

Reviewer: S.Filippi

MSC:

65J10	Numerical solutions to equations with linear operators
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65L20	Stability and convergence of numerical methods for ordinary differential equations

Keywords:

Banach-Steinhaus theorem; Galerkin method; Banach space; Lax-Richtmyer theorem