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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 780769, 11 pages
http://dx.doi.org/10.1155/2014/780769
Research Article

Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method

1Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 689-798, Republic of Korea
2Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea
3Department of Mathematics, Chonnam National University, Gwangju 500-757, Republic of Korea

Received 24 February 2014; Revised 26 May 2014; Accepted 2 June 2014; Published 24 June 2014

Academic Editor: Sofiya Ostrovska

Copyright © 2014 Peyman Hessari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.