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Asymptotic Expansions and Extrapolations of H1-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation

Published online by Cambridge University Press:  21 July 2015

Dongyang Shi ,
Qili Tang  and
Xin Liao
Dongyang Shi
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Qili Tang*
Affiliation:
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
Xin Liao
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
*
*Corresponding author. Email: tql132@163.com (Q. L. Tang)
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Abstract

In this paper, a high-accuracy H1-Galerkin mixed finite element method (MFEM) for strongly damped wave equation is studied by linear triangular finite element. By constructing a suitable extrapolation scheme, the convergence rates can be improved from 𝒪(h) to 𝒪(h3) both for the original variable u in H1(Ω) norm and for the actual stress variable p = ∇ut in H(div;Ω) norm, respectively. Finally, numerical results are presented to confirm the validity of the theoretical analysis and excellent performance of the proposed method.

Keywords

65N3065N15H1-Galerkin MFEMstrongly damped wave equationasymptotic error expansionsextrapolations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 5 , October 2015 , pp. 610 - 624
Copyright
Copyright © Global-Science Press 2015 

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