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 k  -degree 1" class="mathmlsrc">1-s2.0-S0022247X16304267&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304267&_rdoc=1&_issn=0022247X&md5=63a743fc2c76eff98600658f352f371c" title="Click to view the MathML source">(k≥3) finite element methods for the second order elliptic boundary value problem with constant coefficients over a family of uniform rectangular/triangular meshes 1-s2.0-S0022247X16304267&_mathId=si2.gif&_user=111111111&_pii=S0022247X16304267&_rdoc=1&_issn=0022247X&md5=47b353771d97547e83b5c7add65e2ece" title="Click to view the MathML source">T_h${\mathcal{T}}_h$ on a bounded rectangular domain D. The k  -degree finite element estimates are developed for the Green's function and its derivatives. They are employed to explore the relationship among 1-s2.0-S0022247X16304267&_mathId=si3.gif&_user=111111111&_pii=S0022247X16304267&_rdoc=1&_issn=0022247X&md5=d9b3b10fc83d29d1a077c8e32637d278" title="Click to view the MathML source">dist(x,∂D), dist(x,M)$dist(x,\partial D),dist(x,M)$ and the ultraconvergence of k-degree finite element methods at vertex x, where M is the set of corners of D. Numerical examples are conducted to demonstrate our theoretical results.