A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method

Abstract : We studied the pollution-error in the h-version of the finite element method and its effect on the quality of the local error indicators (resp. the quality of the derivatives recovered by local postprocessing) in the interior of the mesh. Here we show that it is possible to construct a-posteriori estimates of the pollution-error in a patch of elements by employing the local error indicators over the entire mesh. We also give an adaptive algorithm for the local control of the pollution-error in a patch of elements of interest.

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