Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM

Bartels, Sören; Carstensen, Carsten

doi:10.1090/S0025-5718-02-01412-6

Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM
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by Sören Bartels and Carsten Carstensen PDF

Math. Comp. 71 (2002), 971-994 Request permission

Abstract:

Averaging techniques are popular tools in adaptive finite element methods since they provide efficient a posteriori error estimates by a simple postprocessing. In the second paper of our analysis of their reliability, we consider conforming $h$-FEM of higher (i.e., not of lowest) order in two or three space dimensions. In this paper, reliablility is shown for conforming higher order finite element methods in a model situation, the Laplace equation with mixed boundary conditions. Emphasis is on possibly unstructured grids, nonsmoothness of exact solutions, and a wide class of local averaging techniques. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides.

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