Abstract
In this paper, a second-order hyperbolic equation is solved by a two-grid algorithm combined with the expanded mixed finite element method. The error estimate of the expanded mixed finite element method with discrete-time scheme is demonstrated. Moreover, we present a two-grid method and analyze its convergence. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H= mathcal{O}(h^{frac{1}{2}}). Finally, some numerical experiments are provided to illustrate the efficiency and accuracy of the proposed method.
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