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Abstract and Applied Analysis
Volume 2013, Article ID 657952, 12 pages
Research Article

An -Galerkin Expanded Mixed Finite Element Approximation of Second-Order Nonlinear Hyperbolic Equations

College of Mathematical Sciences, Shandong Normal University, Jinan 250014, China

Received 11 June 2013; Revised 23 September 2013; Accepted 24 September 2013

Academic Editor: Youyu Wang

Copyright © 2013 Zhaojie Zhou 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.


We investigate an -Galerkin expanded mixed finite element approximation of nonlinear second-order hyperbolic equations, which model a wide variety of phenomena that involve wave motion or convective transport process. This method possesses some features such as approximating the unknown scalar, its gradient, and the flux function simultaneously, the finite element space being free of LBB condition, and avoiding the difficulties arising from calculating the inverse of coefficient tensor. The existence and uniqueness of the numerical solution are discussed. Optimal-order error estimates for this method are proved without introducing curl operator. A numerical example is also given to illustrate the theoretical findings.