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Volume 22, Issue 6
The Derivative Ultraconvergence for Quadratic Triangular Finite Elements

Qiding Zhu & Lingxiong Meng

J. Comp. Math., 22 (2004), pp. 857-864.

Published online: 2004-12

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  • Abstract

This work concerns the ultraconvergence of quadratic finite element approximations of elliptic boundary value problems. A new, discrete least-squares patch recovery technique is proposed to post-process the solution derivatives. Such recovered derivatives are shown to possess ultraconvergence. The keys in the proof are the asymptotic expansion of the bilinear form for the interpolation error and a "localized" symmetry argument. Numerical results are presented to confirm the analysis.

  • Keywords

Ultra-closeness, Superconvergence patch recovery (SPR), Ultraconvergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-857, author = {Zhu , Qiding and Meng , Lingxiong}, title = {The Derivative Ultraconvergence for Quadratic Triangular Finite Elements}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {6}, pages = {857--864}, abstract = {

This work concerns the ultraconvergence of quadratic finite element approximations of elliptic boundary value problems. A new, discrete least-squares patch recovery technique is proposed to post-process the solution derivatives. Such recovered derivatives are shown to possess ultraconvergence. The keys in the proof are the asymptotic expansion of the bilinear form for the interpolation error and a "localized" symmetry argument. Numerical results are presented to confirm the analysis.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10289.html} }
TY - JOUR T1 - The Derivative Ultraconvergence for Quadratic Triangular Finite Elements AU - Zhu , Qiding AU - Meng , Lingxiong JO - Journal of Computational Mathematics VL - 6 SP - 857 EP - 864 PY - 2004 DA - 2004/12 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10289.html KW - Ultra-closeness, Superconvergence patch recovery (SPR), Ultraconvergence. AB -

This work concerns the ultraconvergence of quadratic finite element approximations of elliptic boundary value problems. A new, discrete least-squares patch recovery technique is proposed to post-process the solution derivatives. Such recovered derivatives are shown to possess ultraconvergence. The keys in the proof are the asymptotic expansion of the bilinear form for the interpolation error and a "localized" symmetry argument. Numerical results are presented to confirm the analysis.

Zhu , Qiding and Meng , Lingxiong. (2004). The Derivative Ultraconvergence for Quadratic Triangular Finite Elements. Journal of Computational Mathematics. 22 (6). 857-864. doi:
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