## Pollution-error in the $$h$$-version of the finite-element method and the local quality of a posteriori error estimators.(English)Zbl 0924.65098

Summary: We study the pollution-error in the $$h$$-version of the finite element method and its effect on the local quality of a posteriori error estimators. We show that the pollution-effect in an interior subdomain depends on the relationship between the mesh inside and outside the subdomain and the smoothness of the exact solution. We also demonstrate that it is possible to guarantee the quality of local error estimators in any mesh-patch in the interior of a finite-element mesh by employing meshes which are sufficiently refined outside the patch.

### MSC:

 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74S05 Finite element methods applied to problems in solid mechanics
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