A hybrid discontinuous galerkin method for elliptic problems

Youngmok Jeon, Eun-Jae Park

Research output: Contribution to journalArticle

19 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 Dec 15

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Polynomial approximation
Discontinuous Galerkin Method
Galerkin methods
Elliptic Problems
Boundary element method
Polynomial Approximation
Fluxes
Higher Order Approximation
Second Order Elliptic Equations
Conserve
Boundary Elements
Error Estimates
Norm
Numerical Examples
Cell
Energy

All Science Journal Classification (ASJC) codes

  • Numerical Analysis

Cite this

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A hybrid discontinuous galerkin method for elliptic problems. / Jeon, Youngmok; Park, Eun-Jae.

In: SIAM Journal on Numerical Analysis, Vol. 48, No. 5, 15.12.2010, p. 1968-1983.

Research output: Contribution to journalArticle

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