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

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1384-1407
Journal / PublicationJournal of Scientific Computing
Volume69
Issue number3
Online published17 Jun 2016
Publication statusPublished - Dec 2016

Abstract

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(h2).

Research Area(s)

  • Curved boundary, Curved interface, Discontinuous Galerkin, High order