Asymptotic Expansions and Extrapolations of $H^1$-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation (Advances in Applied Mathematics and Mechanics, 2018)
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 improvedfrom $\mathcal{O}(h)$ to $\mathcal{O}(h^3)$ both for the original variable $u$ in $H^1(Ω)$ norm and forthe actual stress variable $\boldsymbol{P}=∇u_t$ in $H$(div;$Ω$) norm, respectively. Finally, numericalresults are presented to confirm the validity of the theoretical analysis and excellentperformance of the proposed method.