Convergence analysis of two-grid methods for second order hyperbolic equation

Abstract

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 = O ( h 1 2 ) $H= \mathcal{O}(h^{\frac{1}{2}})$ . Finally, some numerical experiments are provided to illustrate the efficiency and accuracy of the proposed method.

Keywords

• Hyperbolic equation
• Expanded mixed finite element method
• Two-grid algorithm
• Error estimate