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2013 An H 1 -Galerkin Expanded Mixed Finite Element Approximation of Second-Order Nonlinear Hyperbolic Equations
Zhaojie Zhou, Weiwei Wang, Huanzhen Chen
Abstr. Appl. Anal. 2013: 1-12 (2013). DOI: 10.1155/2013/657952

Abstract

We investigate an H 1 -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.

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Zhaojie Zhou. Weiwei Wang. Huanzhen Chen. "An H 1 -Galerkin Expanded Mixed Finite Element Approximation of Second-Order Nonlinear Hyperbolic Equations." Abstr. Appl. Anal. 2013 1 - 12, 2013. https://doi.org/10.1155/2013/657952

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 07095211
MathSciNet: MR3129360
Digital Object Identifier: 10.1155/2013/657952

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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