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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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
-
Computational Sciences and Artificial Intelligence in Industry
Generation of Error Indicators for Partial Differential Equations by Machine Learning Methods
Muzalevskiy, Alexey
Neittaanmäki, Pekka
Repin, Sergey
2022
https://doi.org/10.1007/978-3-030-70787-3_6 [Citations: 1]