The Derivative Ultraconvergence for Quadratic Triangular Finite Elements |
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Authors: | Qiding Zhu & Lingxiong Meng |
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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. |
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Keywords: | Ultra-closeness Superconvergence patch recovery (SPR) Ultraconvergence. |
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