Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations

Abstract

The aim of the paper is to propose a second-order accurate Crank-Nicolson scheme for solving semilinear parabolic equations. This scheme combing two-grid finite volume element method involves solving a small nonlinear system on a coarse grid space and a linear system on a fine grid space, which can improve computing efficiency while keeping the accuracy. It means that we can use large time steps in the actual calculation. We further prove the optimal error estimates of the scheme strictly and present numerous simulations to demonstrate the theoretical results.