(untitled) (East Asian Journal on Applied Mathematics, 2020)
A fast time two-mesh finite element algorithm using coarse and fine meshes is applied to the nonlinear Allen-Cahn equation. The stability and convergence of the method are studied and detailed error estimates are provided. Numerical examples confirm the theoretical results. Traditional Galerkin finite element and time two-mesh finite element methods are compared with respect to CPU time, accuracy and coarsening processing. Numerical experiments show the efficiency and effectiveness of the fast algorithm proposed.