Affiliation:
1. School of Mathematics and Statistics, Hengyang Normal University , Hengyang 421008 , Hunan , P. R. China
Abstract
Abstract
In this article, we present a scheme for solving two-dimensional hyperbolic equation using an expanded mixed finite element method. To solve the resulting nonlinear expanded mixed finite element system more efficiently, we propose a two-step two-grid algorithm. Numerical stability and error estimate are proved on both the coarse grid and fine grid. It is shown that the two-grid method can achieve asymptotically optimal approximation as long as the coarse grid size
H
H
and the fine grid size
h
h
satisfy
h
=
O
(
H
(
2
k
+
1
)
⁄
(
k
+
1
)
)
h={\mathcal{O}}\left({H}^{\left(2k+1)/\left(k+1)})
(
k
≥
1
k\ge 1
), where
k
k
is the degree of the approximating space for the primary variable. Numerical experiment is presented to demonstrate the accuracy and the efficiency of the proposed method.