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Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient

Journal of Systems Science and Complexity volume 23, pages 467–483 (2010)Cite this article

Abstract

This paper applies bilinear immersed finite elements (IFEs) in the interior penalty discontinuous Galerkin (DG) methods for solving a second order elliptic equation with discontinuous coefficient. A discontinuous bilinear IFE space is constructed and applied to both the symmetric and nonsymmetric interior penalty DG formulations. The new methods can solve an interface problem on a Cartesian mesh independent of the interface with local refinement at any locations needed even if the interface has a nontrivial geometry. Numerical examples are provided to show features of these methods.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Xiaoming He & Tao Lin

  2. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

    Yanping Lin

  3. Department of Mathematical and Statistics Science, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Yanping Lin

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  1. Xiaoming He
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  2. Tao Lin
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Correspondence to Xiaoming He.

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This research is supported by NSF grant DMS-0713763, the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 501709), the AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics, and NSERC (Canada), and this article is dedicated to Professor David Russell’s 70th birthday.

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He, X., Lin, T. & Lin, Y. Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient. J Syst Sci Complex 23, 467–483 (2010). https://doi.org/10.1007/s11424-010-0141-z

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  • DOI: https://doi.org/10.1007/s11424-010-0141-z

Key words

  • Adaptive mesh
  • discontinuous Galerkin
  • immersed interface
  • interface problems
  • penalty