Journal of Applied Mathematics
Volume 2012 (2012), Article ID 245051, 16 pages
http://dx.doi.org/10.1155/2012/245051
Research Article

Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations

JongKyum Kwon, Soorok Ryu, Philsu Kim, and Sang Dong Kim

Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea

Received 8 August 2011; Accepted 2 November 2011

Academic Editor: Massimiliano Ferronato

Copyright © 2012 JongKyum Kwon 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 uniform bounds on eigenvalues of 𝖡 ℎ − 1 2 𝖠 𝑁 2 are shown both analytically and numerically by the 𝒫 1 finite element preconditioner 𝖡 ℎ − 1 2 for the Legendre spectral element system 𝖠 𝑁 2 𝐮 = 𝐟 which is arisen from a coupled elliptic system occurred by an optimal control problem. The finite element preconditioner is corresponding to a leading part of the coupled elliptic system.