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Volume 1, Issue 3
A Type of Finite Element Gradient Recovery Method Based on Vertex-Edge-Face Interpolation: The Recovery Technique and Superconvergence Property

Qun Lin & Hehu Xie

DOI: 10.4208/eajam.251210.250411a

East Asian J. Appl. Math., 1 (2011), pp. 248-263.

Published online: 2018-02

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  • Abstract

In this paper, a new type of gradient recovery method based on vertex-edge-face interpolation is introduced and analyzed. This method gives a new way to recover gradient approximations and has the same simplicity, efficiency, and superconvergence properties as those of superconvergence patch recovery method and polynomial preserving recovery method. Here, we introduce the recovery technique and analyze its superconvergence properties. We also show a simple application in the a posteriori error estimates. Some numerical examples illustrate the effectiveness of this recovery method.

  • Keywords

Finite element method, least-squares fitting, vertex-edge-face interpolation, superconvergence, a posteriori error estimate.

  • AMS Subject Headings

65N30, 65N12, 65N15, 65D10, 74S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-1-248, author = {}, title = {A Type of Finite Element Gradient Recovery Method Based on Vertex-Edge-Face Interpolation: The Recovery Technique and Superconvergence Property}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {3}, pages = {248--263}, abstract = {

In this paper, a new type of gradient recovery method based on vertex-edge-face interpolation is introduced and analyzed. This method gives a new way to recover gradient approximations and has the same simplicity, efficiency, and superconvergence properties as those of superconvergence patch recovery method and polynomial preserving recovery method. Here, we introduce the recovery technique and analyze its superconvergence properties. We also show a simple application in the a posteriori error estimates. Some numerical examples illustrate the effectiveness of this recovery method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.251210.250411a}, url = {http://global-sci.org/intro/article_detail/eajam/10907.html} }
TY - JOUR T1 - A Type of Finite Element Gradient Recovery Method Based on Vertex-Edge-Face Interpolation: The Recovery Technique and Superconvergence Property JO - East Asian Journal on Applied Mathematics VL - 3 SP - 248 EP - 263 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.251210.250411a UR - https://global-sci.org/intro/article_detail/eajam/10907.html KW - Finite element method, least-squares fitting, vertex-edge-face interpolation, superconvergence, a posteriori error estimate. AB -

In this paper, a new type of gradient recovery method based on vertex-edge-face interpolation is introduced and analyzed. This method gives a new way to recover gradient approximations and has the same simplicity, efficiency, and superconvergence properties as those of superconvergence patch recovery method and polynomial preserving recovery method. Here, we introduce the recovery technique and analyze its superconvergence properties. We also show a simple application in the a posteriori error estimates. Some numerical examples illustrate the effectiveness of this recovery method.

Qun Lin & Hehu Xie. (1970). A Type of Finite Element Gradient Recovery Method Based on Vertex-Edge-Face Interpolation: The Recovery Technique and Superconvergence Property. East Asian Journal on Applied Mathematics. 1 (3). 248-263. doi:10.4208/eajam.251210.250411a
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