A hybrid discontinuous galerkin method for elliptic problems

Youngmok Jeon, Eun Jae Park

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

A new family of hybrid discontinuous Galerkin methods is studied for second-order elliptic equations. Our proposed method is a generalization of the cell boundary element (CBE) method [Y. Jeon and E.-J. Park, Appl. Numer. Math., 58 (2008), pp. 800-814], which allows high order polynomial approximations. Our method can be viewed as a hybridizable discontinuous Galerkin method [B. Cockburn, J. Gopalakrishnan, and R. Lazarov, SIAM J. Numer. Anal., 47 (2009), pp. 1319-1365] using a Bauman-Oden-type local solver. The method conserves the mass in each element and the average flux is continuous across the interelement boundary for even-degree polynomial approximations. Optimal order error estimates measured in the energy norm are proved. Numerical examples are presented to show the performance of the method.

Original languageEnglish
Pages (from-to)1968-1983
Number of pages16
JournalSIAM Journal on Numerical Analysis
Volume48
Issue number5
DOIs
Publication statusPublished - 2010

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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