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Volume 1, Issue 1
Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals

Zhimin Zhang

DOI: 10.4208/ijnam.OA-2004-1101

Int. J. Numer. Anal. Mod., 1 (2004), pp. 1-24.

Published online: 2004-01

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  • Abstract

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under quadrilateral meshes. It has been proven that the recovered gradient converges at a rate $O(h^{1+\rho})$ for $\rho = min(\alpha, 1)$, when the mesh is distorted $O(h^{1+\alpha})$ ($\alpha > 0$) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

  • Keywords

Finite element method, quadrilateral mesh, gradient recovery, superconvergence, a posteriori error estimate.

  • AMS Subject Headings

65N30, 65N15, 41A10, 41A25, 41A27, 41A63

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zzhang@math.wayne.edu (Zhimin Zhang)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-1-1, author = {Zhang , Zhimin}, title = {Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2004}, volume = {1}, number = {1}, pages = {1--24}, abstract = {

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under quadrilateral meshes. It has been proven that the recovered gradient converges at a rate $O(h^{1+\rho})$ for $\rho = min(\alpha, 1)$, when the mesh is distorted $O(h^{1+\alpha})$ ($\alpha > 0$) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam.OA-2004-1101}, url = {http://global-sci.org/intro/article_detail/ijnam/963.html} }
TY - JOUR T1 - Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals AU - Zhang , Zhimin JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 24 PY - 2004 DA - 2004/01 SN - 1 DO - http://doi.org/10.4208/ijnam.OA-2004-1101 UR - https://global-sci.org/intro/article_detail/ijnam/963.html KW - Finite element method, quadrilateral mesh, gradient recovery, superconvergence, a posteriori error estimate. AB -

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under quadrilateral meshes. It has been proven that the recovered gradient converges at a rate $O(h^{1+\rho})$ for $\rho = min(\alpha, 1)$, when the mesh is distorted $O(h^{1+\alpha})$ ($\alpha > 0$) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

Zhimin Zhang. (1970). Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals. International Journal of Numerical Analysis and Modeling. 1 (1). 1-24. doi:10.4208/ijnam.OA-2004-1101
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