Towards optimal finite element error estimates for the penalized Dirichlet problem in a domain with curved boundary

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• 作者：Dione Ibrahima ^{ibrahima.dione.1@ulaval.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Elliptic equations ; Curved boundary ; Finite element ; Dirichlet boundary conditions ; Penalty method
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：71
• 期：1
• 页码：76-84
• 全文大小：402 K

文摘

We consider the finite element approximation of an elliptic problem with homogeneous Dirichlet boundary conditions on a curved boundary and imposed using the penalty method. We establish optimal H¹$H^1$ error estimates with suitable assumptions on the penalty parameter ε$\epsilon$ as a function of the elements size h$h$. Our focus is on establishing these results with least restrictive assumptions possible on this dependency.