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Volume 7, Issue 5
Asymptotic Expansions and Extrapolations of $H^1$-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation

Dongyang Shi, Qili Tang & Xin Liao

Adv. Appl. Math. Mech., 7 (2015), pp. 610-624.

Published online: 2018-05

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  • 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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@Article{AAMM-7-610, author = {Dongyang and Shi and and 19790 and and Dongyang Shi and Qili and Tang and and 19791 and and Qili Tang and Xin and Liao and and 19792 and and Xin Liao}, title = {Asymptotic Expansions and Extrapolations of $H^1$-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m90}, url = {http://global-sci.org/intro/article_detail/aamm/12066.html} }
TY - JOUR T1 - Asymptotic Expansions and Extrapolations of $H^1$-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation AU - Shi , Dongyang AU - Tang , Qili AU - Liao , Xin JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 610 EP - 624 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2013.m90 UR - https://global-sci.org/intro/article_detail/aamm/12066.html KW - AB -

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.

Dongyang Shi, Qili Tang & Xin Liao. (1970). Asymptotic Expansions and Extrapolations of $H^1$-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation. Advances in Applied Mathematics and Mechanics. 7 (5). 610-624. doi:10.4208/aamm.2013.m90
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