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Abstract and Applied Analysis
Volume 2014, Article ID 803615, 6 pages
http://dx.doi.org/10.1155/2014/803615
Research Article

A Two-Grid Finite Element Method for a Second-Order Nonlinear Hyperbolic Equation

1School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China
2School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China

Received 6 December 2013; Accepted 28 January 2014; Published 5 March 2014

Academic Editor: Xinguang Zhang

Copyright © 2014 Chuanjun Chen 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

We present a two-grid finite element scheme for the approximation of a second-order nonlinear hyperbolic equation in two space dimensions. In the two-grid scheme, the full nonlinear problem is solved only on a coarse grid of size . The nonlinearities are expanded about the coarse grid solution on the fine gird of size . The resulting linear system is solved on the fine grid. Some a priori error estimates are derived with the -norm for the two-grid finite element method. Compared with the standard finite element method, the two-grid method achieves asymptotically same order as long as the mesh sizes satisfy .