THE DERIVATIVE ULTRACONVERGENCE FOR QUADRATIC TRIANGULAR FINITE ELEMENTS

• 来源期刊: 计算数学(英文版)
• 关键词: Ultra-closeness Superconvergence patch recovery (SPR) Ultraconvergence.
• 年，卷（期）: 2004,（6）
• 页码范围: 857-864
• 页数: 8页
• 语种: 英文

摘要

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 shownto 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.