Analysis of two‐grid discretization scheme for semilinear hyperbolic equations by mixed finite element methods

摘要

> In this paper, the full discrete scheme of mixed finite element approximation is introduced for semilinear hyperbolic equations. To solve the nonlinear problem efficiently, two two‐grid algorithms are developed and analyzed. In this approach, the nonlinear system is solved on a coarse mesh with width H , and the linear system is solved on a fine mesh with width h ? H . Error estimates and convergence results of two‐grid method are derived in detail. It is shown that if we choose H = O ( h 1 3 ) in the first algorithm and H = O ( h 1