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Analysis of recovery type a posteriori error estimators for mildly structured grids. (English) Zbl 1050.65103
Authors’ abstract: Some recovery type error estimators for linear finite elements are analyzed under \(O(h^{1+\alpha})\) (\(\alpha > 0\)) regular grids. Superconvergence of order \(O(h^{1+\rho})\) (\(0<\rho\leq\alpha\)) is established for recovered gradients by three different methods. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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