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Volume 25, Issue 6
A Robust Finite Element Method for a 3-D Elliptic Singular Perturbation Problem

Ming Wang & Xiangrui Meng

J. Comp. Math., 25 (2007), pp. 631-644.

Published online: 2007-12

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  • Abstract

This paper proposes a robust finite element method for a three-dimensional fourth-order elliptic singular perturbation problem. The method uses the three-dimensional Morley element and replaces the finite element functions in the part of bilinear form corresponding to the second-order differential operator by a suitable approximation. To give such an approximation, a convergent nonconforming element for the second-order problem is constructed. It is shown that the method converges uniformly in the perturbation parameter.

  • Keywords

Finite element, Singular perturbation problem.

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-631, author = {Ming Wang and Xiangrui Meng}, title = {A Robust Finite Element Method for a 3-D Elliptic Singular Perturbation Problem}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {6}, pages = {631--644}, abstract = {

This paper proposes a robust finite element method for a three-dimensional fourth-order elliptic singular perturbation problem. The method uses the three-dimensional Morley element and replaces the finite element functions in the part of bilinear form corresponding to the second-order differential operator by a suitable approximation. To give such an approximation, a convergent nonconforming element for the second-order problem is constructed. It is shown that the method converges uniformly in the perturbation parameter.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8719.html} }
TY - JOUR T1 - A Robust Finite Element Method for a 3-D Elliptic Singular Perturbation Problem AU - Ming Wang & Xiangrui Meng JO - Journal of Computational Mathematics VL - 6 SP - 631 EP - 644 PY - 2007 DA - 2007/12 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8719.html KW - Finite element, Singular perturbation problem. AB -

This paper proposes a robust finite element method for a three-dimensional fourth-order elliptic singular perturbation problem. The method uses the three-dimensional Morley element and replaces the finite element functions in the part of bilinear form corresponding to the second-order differential operator by a suitable approximation. To give such an approximation, a convergent nonconforming element for the second-order problem is constructed. It is shown that the method converges uniformly in the perturbation parameter.

Ming Wang and Xiangrui Meng. (2007). A Robust Finite Element Method for a 3-D Elliptic Singular Perturbation Problem. Journal of Computational Mathematics. 25 (6). 631-644. doi:
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