## Taiwanese Journal of Mathematics

### High-order Discontinuous Galerkin Method for Solving Elliptic Interface Problems

#### 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 $Q^k$-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.

#### Article information

Source
Taiwanese J. Math., Volume 20, Number 5 (2016), 1185-1202.

Dates
First available in Project Euclid: 1 July 2017

https://projecteuclid.org/euclid.twjm/1498874524

Digital Object Identifier
doi:10.11650/tjm.20.2016.7612

Mathematical Reviews number (MathSciNet)
MR3555896

Zentralblatt MATH identifier
1357.65255

#### Citation

Chen, Min-Hung; Wu, Rong-Jhao. High-order Discontinuous Galerkin Method for Solving Elliptic Interface Problems. Taiwanese J. Math. 20 (2016), no. 5, 1185--1202. doi:10.11650/tjm.20.2016.7612. https://projecteuclid.org/euclid.twjm/1498874524

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