A new fictitious domain method: Optimal convergence without cut elements

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• 作者：Alexei Lozinski ^{alexei.lozinski@univ-fcomte.fr" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Comptes Rendus Mathematique
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：354
• 期：7
• 页码：741-746
• 全文大小：388 K

文摘

We present a method of the fictitious domain type for the Poisson–Dirichlet problem. The computational mesh is obtained from a background (typically uniform Cartesian) mesh by retaining only the elements intersecting the domain where the problem is posed. The resulting mesh does not thus fit the boundary of the problem domain. Several finite element methods (XFEM, CutFEM) adapted to such meshes have been recently proposed. The originality of the present article consists in avoiding integration over the elements cut by the boundary of the problem domain, while preserving the optimal convergence rates, as confirmed by both the theoretical estimates and the numerical results.