In 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.