High-order discontinuous Galerkin method for solving Elliptic interface problems

Min Hung Chen, Rong Jhao Wu

Research output: Contribution to journalArticle

Abstract

In this study, we develop a high-order accurate discontinuous Galerkin scheme using curvilinear quadrilateral elements for solving elliptic interface problems. To maintain accuracy for curvilinear quadrilateral elements with Qk-polynomial basis functions, we select Legendre-Gauss-Lobatto quadrature rules with k + 2 integration points, including end points, on each edge. Numerical experiments show quadrature rules are appropriate and the numerical solution converges with the order k + 1. Moreover, we implement the Uzawa method to rewrite the original linear system into smaller linear systems. The resulting method is three times faster than the original system. We also find that high-order methods are more efficient than low-order methods. Based on this result, we conclude that under the condition of limited computational resources, the best approach for achieving optimal accuracy is to solve a problem using the coarsest mesh and local spaces with the highest degree of polynomials.

Original languageEnglish
Pages (from-to)1185-1202
Number of pages18
JournalTaiwanese Journal of Mathematics
Volume20
Issue number5
DOIs
Publication statusPublished - 2016 Jan 1

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Interface Problems
Discontinuous Galerkin Method
Elliptic Problems
Quadrilateral Element
Quadrature Rules
Higher Order
Linear Systems
Gauss Quadrature
Polynomial Basis
Discontinuous Galerkin
High-order Methods
Legendre
End point
Polynomial function
Basis Functions
Numerical Experiment
Numerical Solution
Mesh
Converge
Resources

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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High-order discontinuous Galerkin method for solving Elliptic interface problems. / Chen, Min Hung; Wu, Rong Jhao.

In: Taiwanese Journal of Mathematics, Vol. 20, No. 5, 01.01.2016, p. 1185-1202.

Research output: Contribution to journalArticle

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