Saturation and Reliable Hierarchical a Posteriori Morley Finite Element Error Control

Saturation and Reliable Hierarchical a Posteriori Morley Finite Element Error Control

Year:    2018

Author:    Carsten Carstensen, Dietmar Gallistl, Yunqing Huang

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 6 : pp. 833–844

Abstract

This paper proves the saturation assumption for the nonconforming Morley finite element discretization of the biharmonic equation. This asserts that the error of the Morley approximation under uniform refinement is strictly reduced by a contraction factor smaller than one up to explicit higher-order data approximation terms. The refinement has at least to bisect any edge such as red refinement or 3-bisections on any triangle.

This justifies a hierarchical error estimator for the Morley finite element method, which simply compares the discrete solutions of one mesh and its red-refinement. The related adaptive mesh-refining strategy performs optimally in numerical experiments. A remark for Crouzeix-Raviart nonconforming finite element error control is included.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1705-m2016-0549

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 6 : pp. 833–844

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Saturation Hierarchical error estimation Finite element Nonconforming Biharmonic Morley Kirchhoff plate Crouzeix-Raviart.

Author Details

Carsten Carstensen

Dietmar Gallistl

Yunqing Huang

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