Superconvergence Analysis of Galerkin Finite Element Method for the Nonlinear Parabolic Integro-Differential Equation
The Crank-Nicolson(CN)fully discrete scheme of conforming Galerkin finite element method was mainly studied for the nonlinear parabolic integro-differential equation.By estimating the nonlinear term rigorously and using combination trick of the interpolation and projection,the supercloseness of order O(h2+r2)in L∞(H1)norm was derived.Further,the global superconvergence result was obtained through interpolated post-processing technique,which covers the shortage in the previous literature.At the same time,a numerical example was provided to verify the correctness of the theoretical analysis and the high efficient of the proposed method.
nonlinear parabolic integro-differential equationconforming Galerkin finite element methodsuperclosenesssuperconvergence
万方数据
维普
