Two Dangers to Avoid When Using Gradient Recovery Methods for Finite Element Error Estimation and Adaptivity
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Submission date: 22. Aug. 2006
MSC-Numbers: 65N15, 65N30, 65N50
Keywords and phrases: finite element methods, gradient recovery, a posteriori error estimation
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Gradient recovery methods for a posteriori error estimation in the finite element method are justifiably popular. They are relatively simple to implement, cheap in terms of storage and computational cost, and generally provide efficient and reliable global and local error estimates for adaptive algorithms. In this report we highlight two practical difficulties which can arise when such techniques are used naively, difficulties which can lead to arbitrarily poor performance of the error estimator both in terms of estimating the true error and in effectively guiding the adaptive refinement process.