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A multiscale a posteriori error estimate. (English) Zbl 1091.76030

Summary: We introduce a hierarchic a posteriori error estimate for singularly perturbed reaction-diffusion problems. The estimator is based on a Petrov-Galerkin method in which the trial space is enriched with nonpolynomial functions or multiscale functions. We study the equivalence between the a posteriori estimate and the exact error in the energy norm. Moreover, we prove a relationship between the hierarchic estimator and an explicit residual estimator. The approach provides accurate estimates for the boundary layer regions which is confirmed by numerical experiments.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76V05 Reaction effects in flows
76R50 Diffusion
65N15 Error bounds for boundary value problems involving PDEs

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References:

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