Two-Grid Finite Element Methods of Crank-Nicolson Galerkin Approximation for a Nonlinear Parabolic Equation

Abstract

Two-grid finite element methods with the Crank-Nicolson Galerkin scheme for nonlinear parabolic equations are studied. It is shown that the methods have convergence order $\mathcal{O}$($h$ + $H$² + (∆$t$)²) in $H$¹-norm, so that a larger time step can be used in numerical calculations. In addition to saving computing time, the algorithms provide a good approximation of the problem solution and numerical examples confirm their efficiency.