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Volume 36, Issue 6
Saturation and Reliable Hierarchical a Posteriori Morley Finite Element Error Control

Carsten Carstensen, Dietmar Gallistl & Yunqing Huang

DOI: 10.4208/jcm.1705-m2016-0549

J. Comp. Math., 36 (2018), pp. 833-844.

Published online: 2018-08

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M12, 65M60, 65N25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

cc@math.hu-berlin.de (Carsten Carstensen)

dietmar.gallistl@uni-jena.de (Dietmar Gallistl)

huangyq@xtu.edu.cn (Yunqing Huang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-833, author = {Carstensen , CarstenGallistl , Dietmar and Huang , Yunqing}, title = {Saturation and Reliable Hierarchical a Posteriori Morley Finite Element Error Control}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1705-m2016-0549}, url = {http://global-sci.org/intro/article_detail/jcm/12604.html} }
TY - JOUR T1 - Saturation and Reliable Hierarchical a Posteriori Morley Finite Element Error Control AU - Carstensen , Carsten AU - Gallistl , Dietmar AU - Huang , Yunqing JO - Journal of Computational Mathematics VL - 6 SP - 833 EP - 844 PY - 2018 DA - 2018/08 SN - 36 DO - http://doi.org/10.4208/jcm.1705-m2016-0549 UR - https://global-sci.org/intro/article_detail/jcm/12604.html KW - Saturation, Hierarchical error estimation, Finite element, Nonconforming, Biharmonic, Morley, Kirchhoff plate, Crouzeix-Raviart. AB -

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.

Carstensen , CarstenGallistl , Dietmar and Huang , Yunqing. (2018). Saturation and Reliable Hierarchical a Posteriori Morley Finite Element Error Control. Journal of Computational Mathematics. 36 (6). 833-844. doi:10.4208/jcm.1705-m2016-0549
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