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Volume 32, Issue 6
Uniformly Convergent Nonconforming Element for 3-D Fourth Order Elliptic Singular Perturbation Problem

Hongru Chen & Shaochun Chen

DOI: 10.4208/jcm.1405-m4303

J. Comp. Math., 32 (2014), pp. 687-695.

Published online: 2014-12

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  • Abstract

In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming $C^0$-cuboid element converges in the energy norm uniformly with respect to the perturbation parameter.

  • Keywords

Nonconforming finite element, Singular perturbation problem, Uniform error estimates.

  • AMS Subject Headings

65N12, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-687, author = {Hongru Chen and Shaochun Chen}, title = {Uniformly Convergent Nonconforming Element for 3-D Fourth Order Elliptic Singular Perturbation Problem}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {6}, pages = {687--695}, abstract = {

In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming $C^0$-cuboid element converges in the energy norm uniformly with respect to the perturbation parameter.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1405-m4303}, url = {http://global-sci.org/intro/article_detail/jcm/8409.html} }
TY - JOUR T1 - Uniformly Convergent Nonconforming Element for 3-D Fourth Order Elliptic Singular Perturbation Problem AU - Hongru Chen & Shaochun Chen JO - Journal of Computational Mathematics VL - 6 SP - 687 EP - 695 PY - 2014 DA - 2014/12 SN - 32 DO - http://doi.org/10.4208/jcm.1405-m4303 UR - https://global-sci.org/intro/article_detail/jcm/8409.html KW - Nonconforming finite element, Singular perturbation problem, Uniform error estimates. AB -

In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming $C^0$-cuboid element converges in the energy norm uniformly with respect to the perturbation parameter.

Hongru Chen and Shaochun Chen. (2014). Uniformly Convergent Nonconforming Element for 3-D Fourth Order Elliptic Singular Perturbation Problem. Journal of Computational Mathematics. 32 (6). 687-695. doi:10.4208/jcm.1405-m4303
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