Saturation and reliable hierarchical a posteriori Morley finite element error control

C. Carstensen, D. Gallistl, Y. Huang

Research output: Contribution to journalArticleAcademicpeer-review

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.
Original languageEnglish
Pages (from-to)833-844
Number of pages12
JournalJournal of Computational Mathematics
Volume36
Issue number6
DOIs
Publication statusPublished - 2018

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Error Control
Saturation
Refinement
Finite Element
Bisect
Nonconforming Finite Element
Adaptive Mesh
Refining
Biharmonic Equation
Bisection
Error Estimator
Finite Element Discretization
Approximation
Justify
Finite element method
Contraction
Triangle
Strictly
Finite Element Method
Numerical Experiment

Cite this

Carstensen, C. ; Gallistl, D. ; Huang, Y. / Saturation and reliable hierarchical a posteriori Morley finite element error control. In: Journal of Computational Mathematics. 2018 ; Vol. 36, No. 6. pp. 833-844.
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Saturation and reliable hierarchical a posteriori Morley finite element error control. / Carstensen, C.; Gallistl, D.; Huang, Y.

In: Journal of Computational Mathematics, Vol. 36, No. 6, 2018, p. 833-844.

Research output: Contribution to journalArticleAcademicpeer-review

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