Analysis of two-grid method for second-order hyperbolic equation by expanded mixed finite element methods

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 HH and the fine grid size hh satisfy h=O(H(2k+1)⁄(k+1))h={\mathcal{O}}\left({H}^{\left(2k+1)/\left(k+1)}) (k≥1k\ge 1), where kk 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.

Keywords

• hyperbolic equation
• expanded mixed finite element method
• two-grid method
• error estimate
• 35l20
• 65m60