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Volume 32, Issue 2
Convergence and Superconvergence Analysis of Lagrange Rectangular Elements with Any Order on Arbitrary Rectangular Meshes

Mingxia Li, Xiaofei Guan & Shipeng Mao

DOI: 10.4208/jcm.1310-FE2

J. Comp. Math., 32 (2014), pp. 169-182.

Published online: 2014-04

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  • Abstract

This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.

  • Keywords

Lagrange interpolation, Anisotropic error bounds, Arbitrary rectangular meshes, Orthogonal expansion, Superconvergence.

  • AMS Subject Headings

65N12, 65N15, 65N30, 65N50.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-32-169, author = {Mingxia Li, Xiaofei Guan and Shipeng Mao}, title = {Convergence and Superconvergence Analysis of Lagrange Rectangular Elements with Any Order on Arbitrary Rectangular Meshes}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {2}, pages = {169--182}, abstract = {

This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1310-FE2}, url = {http://global-sci.org/intro/article_detail/jcm/9876.html} }
TY - JOUR T1 - Convergence and Superconvergence Analysis of Lagrange Rectangular Elements with Any Order on Arbitrary Rectangular Meshes AU - Mingxia Li, Xiaofei Guan & Shipeng Mao JO - Journal of Computational Mathematics VL - 2 SP - 169 EP - 182 PY - 2014 DA - 2014/04 SN - 32 DO - http://doi.org/10.4208/jcm.1310-FE2 UR - https://global-sci.org/intro/article_detail/jcm/9876.html KW - Lagrange interpolation, Anisotropic error bounds, Arbitrary rectangular meshes, Orthogonal expansion, Superconvergence. AB -

This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.

Mingxia Li, Xiaofei Guan and Shipeng Mao. (2014). Convergence and Superconvergence Analysis of Lagrange Rectangular Elements with Any Order on Arbitrary Rectangular Meshes. Journal of Computational Mathematics. 32 (2). 169-182. doi:10.4208/jcm.1310-FE2
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