Abstract and Applied Analysis

Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method

Abstract

The aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method. First, we develop an algorithm for the elliptic interface problem defined in a rectangular domain with a line interface. By using the Gordon-Hall transformation, we generalize it to a domain with a curve boundary and a curve interface. The spectral element collocation method is then employed to complex geometries; that is, we decompose the domain into some nonoverlaping subdomains and the spectral collocation solution is sought in each subdomain. We give some numerical experiments to show efficiency of our algorithm and its spectral convergence.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 780769, 11 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606199

Digital Object Identifier
doi:10.1155/2014/780769

Mathematical Reviews number (MathSciNet)
MR3228088

Zentralblatt MATH identifier
07023047

Citation

Hessari, Peyman; Kim, Sang Dong; Shin, Byeong-Chun. Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 780769, 11 pages. doi:10.1155/2014/780769. https://projecteuclid.org/euclid.aaa/1412606199

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