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

Abstract

AbstractIn 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.