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

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 = {Shi , Dongyang and Tang , Qili and Liao , Xin}, 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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