SATURATION AND RELIABLE HIERARCHICAL A POSTERIORI MORLEY FINITE ELEMENT ERROR CONTROL

Carsten Carstensen1, Dietmar Gallistl2, Yunqing Huang3

1. 1. Humboldt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany;
2. Department of Applied Mathematics, University of Twente, P. O. Box 217, 7500 AE Enschede The Netherlands;
3. Institute for Computational and Applied Mathematics and Hunan Key Laboratory for Computation & Simulation in Science & Engineering, Xiangtan University, Xiangtan 411105, China
• Received:2016-02-22 Revised:2017-02-09 Online:2018-11-15 Published:2018-11-15
• Supported by:

This work was supported by the Chinesisch-Deutsches Zentrum through project GZ578. The work was initiated while the first two authors enjoyed their pleasant visit to the Hunan Key Laboratory for Computation & Simulation in Science & Engineering of the Xiangtan University in China in 2013. The revision was accomplished during a research stay at the Hausdorff Institute for Mathematics (Bonn) in 2017. The kind hospitality is thankfully acknowledged. The third author was also supported by NSFC key project 91430213.

Carsten Carstensen, Dietmar Gallistl, Yunqing Huang. SATURATION AND RELIABLE HIERARCHICAL A POSTERIORI MORLEY FINITE ELEMENT ERROR CONTROL[J]. Journal of Computational Mathematics, 2018, 36(6): 833-844.

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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