A High Order HDG Method for Curved-Interface Problems Via Approximations from Straight Triangulations

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• 作者：Weifeng Qiu ; Manuel Solano ; Patrick Vega
• 关键词：Discontinuous Galerkin ; High order ; Curved boundary ; Curved interface
• 刊名：Journal of Scientific Computing
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：69
• 期：3
• 页码：1384-1407
• 全文大小：2,913 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691
• 卷排序：69

文摘

We propose a novel technique to solve elliptic problems involving a non-polygonal interface/boundary. It is based on a high order hybridizable discontinuous Galerkin method where the mesh does not exactly fit the domain. We first study the case of a curved-boundary value problem with mixed boundary conditions since it is crucial to understand the applicability of the technique to curved interfaces. The Dirichlet data is approximated by using the transferring technique developed in a previous paper. The treatment of the Neumann data is new. We then extend these ideas to curved interfaces. We provide numerical results showing that, in order to obtain optimal high order convergence, it is desirable to construct the computational domain by interpolating the boundary/interface using piecewise linear segments. In this case the distance of the computational domain to the exact boundary is only \(O(h^2)\).