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

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-edgeface 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

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-1-248, author = {Qun Lin and Hehu Xie}, 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-edgeface 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 AU - Qun Lin & Hehu Xie 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 KW - least-squares fitting KW - vertex-edge-face interpolation KW - superconvergence KW - a posteriori error estimate AB -

In this paper, a new type of gradient recovery method based on vertex-edgeface 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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