Crank-Nicolson Method of a Two-Grid Finite Volume Element Algorithm for Nonlinear Parabolic Equations

Abstract

A two-grid finite volume element algorithm based on Crank-Nicolson scheme for nonlinear parabolic equations is proposed. In this method, the nonlinear problem is solved on a coarse grid of size $H$ and a linear problem is considered on a fine grid of size $h$ by using the coarse-grid solution and one Newton iteration. This helps to improve the computing efficiency while keeping the accuracy. It is proved that the two-grid method can achieve asymptotically optimal error estimates in spaces and second order accuracy in time. Numerical results are consistent with the theoretical findings.