Implicit a posteriori error estimation using patch recovery techniques

Tamás Horváth and Ferenc Izsák
  • 1 Széchenyi University
  • 2 Eötvös Loránd University
  • 3 University of Twente

Abstract

We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.

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