Asymptotic Expansions and Extrapolations of $H^1$-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation
Year: 2015
Author: Dongyang Shi, Qili Tang, Xin Liao
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 5 : pp. 610–624
Abstract
In this paper, a high-accuracy $H^1$-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 $\mathcal{O}(h)$ to $\mathcal{O}(h^3)$ both for the original variable $u$ in $H^1(Ω)$ norm and for the actual stress variable $\boldsymbol{P}=∇u_t$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m90
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 5 : pp. 610–624
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
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