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A posteriori error analysis for elliptic PDEs on domains with complicated structures. (English) Zbl 1049.65120
The authors are concerned with a mixed boundary value problem for the Poisson equation on a triangulated polygonal domain with holes of a size of mesh width at most. They reformulate the whole finite element method for such special domains and carry out some reliable and efficient a posteriori estimations. They pay a lot of attention to the technical difficulties involved in the numerical approximation of the domain and also to their influence on the constants which enter into the estimations.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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