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Error analysis of local refinements of polygonal domains. (English) Zbl 0625.65094

This paper presents a thorough analysis of the local refinements of polygonal domains using weighted Sobolev spaces. The estimates obtained indicate the dependence of the approximation properties on the singularities of the solution. Theorems are presented for the existence and an estimation of the error in the solution.
Reviewer: P.K.Mahanti

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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