The local ultraconvergence for high-degree Galerkin finite element methods

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• 作者：Wen-ming He^a ; ^{he_wenming@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; Junzhi Cui^b ; ^{cjz@lsec.cc.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Jiangman Shen^a
• 关键词：Elliptic problem ; Ultraconvergence ; Derivative recovery operator ; Displacement ; Derivative
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：62-86
• 全文大小：543 K

文摘

In this paper, we investigate the local ultraconvergence of <em>k  em>-degree (k≥3)$(k\ge 3)$ finite element methods for the second order elliptic boundary value problem with constant coefficients over a family of uniform rectangular/triangular meshes T_h${\mathcal{T}}_h$ on a bounded rectangular domain <em>Dem>. The <em>k  em>-degree finite element estimates are developed for the Green's function and its derivatives. They are employed to explore the relationship among dist(x,∂D), dist(x,M)$dist(x,\partial D),dist(x,M)$ and the ultraconvergence of <em>kem>-degree finite element methods at vertex <em>xem>, where <em>Mem> is the set of corners of <em>Dem>. Numerical examples are conducted to demonstrate our theoretical results.