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An introduction to the analysis of the error in the finite element method for second-order elliptic boundary value problems. (English) Zbl 0577.65096

Numerical analysis, Proc. SERC Summer Sch., Lancaster/Engl. 1984, Lect. Notes Math. 1129, 94-139 (1985).
[For the entire collection see Zbl 0551.00010.]
This paper provides an introduction to the mathematical analysis of the finite element method for second order elliptic boundary value problems. It includes: Some definitions concerning the various function spaces used; two model elliptic boundary value problems; the definitions of the finite element spaces used to approximate the solutions of the boundary value problems; existence, uniqueness and error estimates of the Galerkin method in the context of one of the model problems; local error estimates for the finite element method.
Reviewer: N.F.F.Ebecken

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Citations:

Zbl 0551.00010