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A posteriori estimation of the error in the error estimate. (English) Zbl 0948.74068

Summary: We address the problem of a posteriori estimation of the error in the error estimate. We consider the case of estimates for the error in derivatives, strains, or stresses, which are constructed in terms of locally-computed element error indicators of the element residual, or the least-squares recovery type. The estimates of the error in the error estimate have the same structure as the original error estimates, and are determined by locally averaging (recycling) the original error indicators. The most accurate indicators of the error in the error indicators are obtained by employing a ‘harmonic’ basis in the recycling of the indicators, namely, a basis which locally satisfies the partial differential equation and boundary conditions.

MSC:

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