Sobolev方程的CN全离散化有限元格式

A CRANK-NICOLSON FULLY DISCRETE FINITE ELEMENT FORMULATION FOR THE SOBOLEV EQUATIONS

首先给出Sobolev方程关于时间二阶精度的Crank-Nicolson(CN)时间半离散格式,然后直接从时间二阶精度的CN时间半离散格式出发,构造CN全离散化的有限元格式,并给出这种时间二阶精度的CN全离散化有限元解的误差估计,本文研究方法使得理论证明变得更简便,也是处理Sobolev方程的一种新的尝试.

A semi-discrete formulation in time by Crank-Nicolson method with second-order accu- racy for two-dimensional Sobolev equations is established firstly. And then, the fully discrete finite element （FE） scheme for the Sobolev equation is directly established from the CrankNicolson time semi-discrete formulation. And the error estimates for the fully discrete FE approximate solutions with time second-order are derived. The approaches studied here could make theoretical argumentation simpler and more convenient. And it is a new study attempt for Sobolev equations.