New a posteriori error estimate and quasi-optimal convergence of the adaptive nonconforming Wilson element

详细信息    查看全文

• 作者：Jun Hu^a ; ^{hujun@math.pku.edu.cn" class="auth_mail} ; Longlong Jiang^a ; ^{1001210026@pku.edu.cn" class="auth_mail} ; Zhongci Shi^b ; ^{shi@lsec.cc.ac.cn" class="auth_mail}
• 关键词：Adaptive Wilson element ; A posteriori error estimate ; Optimal convergence
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：1 August, 2014
• 年：2014
• 卷：265
• 期：Complete
• 页码：173-186
• 全文大小：535 K

文摘

In this paper we establish the quasi-optimal convergence of the adaptive nonconforming Wilson element on the rectangular mesh. The main ingredients are a new a posteriori error estimator and a crucial observation that there is some special orthogonality between the conforming part and the nonconforming part in the energy inner product, which helps us to show the quasi-orthogonality and the discrete reliability. Finally we integrate these components in a usual way to achieve the quasi-optimal convergence.