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Volume 26, Issue 4
A Posteriori Estimator of Nonconforming Finite Element Method for Fourth Order Elliptic Perturbation Problems

Shuo Zhang & Ming Wang

J. Comp. Math., 26 (2008), pp. 554-577.

Published online: 2008-08

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  • Abstract

In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an $a posteriori$ error estimator under certain conditions, and give an $h$-version adaptive algorithm based on the error estimation. The local behavior of the estimator is analyzed as well. This estimator works for several nonconforming methods, such as the modified Morley method and the modified Zienkiewicz method, and under some assumptions, it is an optimal one. Numerical examples are reported, with a linear stationary Cahn-Hilliard-type equation as a model problem.

  • Keywords

Fourth order elliptic perturbation problems, Nonconforming finite element method, A posteriori error estimator, Adaptive algorithm, Local behavior.

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-26-554, author = {Shuo Zhang and Ming Wang}, title = {A Posteriori Estimator of Nonconforming Finite Element Method for Fourth Order Elliptic Perturbation Problems}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {4}, pages = {554--577}, abstract = {

In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an $a posteriori$ error estimator under certain conditions, and give an $h$-version adaptive algorithm based on the error estimation. The local behavior of the estimator is analyzed as well. This estimator works for several nonconforming methods, such as the modified Morley method and the modified Zienkiewicz method, and under some assumptions, it is an optimal one. Numerical examples are reported, with a linear stationary Cahn-Hilliard-type equation as a model problem.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8642.html} }
TY - JOUR T1 - A Posteriori Estimator of Nonconforming Finite Element Method for Fourth Order Elliptic Perturbation Problems AU - Shuo Zhang & Ming Wang JO - Journal of Computational Mathematics VL - 4 SP - 554 EP - 577 PY - 2008 DA - 2008/08 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8642.html KW - Fourth order elliptic perturbation problems, Nonconforming finite element method, A posteriori error estimator, Adaptive algorithm, Local behavior. AB -

In this paper, we consider the nonconforming finite element approximations of fourth order elliptic perturbation problems in two dimensions. We present an $a posteriori$ error estimator under certain conditions, and give an $h$-version adaptive algorithm based on the error estimation. The local behavior of the estimator is analyzed as well. This estimator works for several nonconforming methods, such as the modified Morley method and the modified Zienkiewicz method, and under some assumptions, it is an optimal one. Numerical examples are reported, with a linear stationary Cahn-Hilliard-type equation as a model problem.

Shuo Zhang and Ming Wang. (2008). A Posteriori Estimator of Nonconforming Finite Element Method for Fourth Order Elliptic Perturbation Problems. Journal of Computational Mathematics. 26 (4). 554-577. doi:
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