摘要
对剪切板形变问题的全离散误差估计进行了研究 .首先利用Galerkin方法 ,对Ω进行有限元剖分 ,获得两个有限维空间Qh 和Vh 并假设满足Dirichlet边界条件 ,再利用Green定理获得有限元逼近形式 ,并采用Crank -Nicolson格式的一种变形形式对时间进行离散 .根据交替法的思想 ,将这一耦合非线性方程组变成两个独立的非耦合的方程 ,最后利用初值得出在L2 范数下的最优误差估计式 .
In this paper provided is an error estimation for fully-discrete method, which has not been studied yet.Firstly we discretize Ω into finite element,use the Galerkin,and thus obtain two finite dimensional spaces Q h and V h,and a system of ordinary differntial equations,and assume that the function in υ and θ satisfying the Dirichlet bundary conditions.Secondly,we use Green theorem to obtain an expression of finite element approximation of an evolution. Then by adopting Crank-Nicolson format, we use a derivative format to discretize time.According to the alternation method,after transforming change these coupling nonlinear equations into two separate noncoupling equations. Finally,we use initial value to obtain that result is the optimal error estimates in the L 2-norm.
出处
《西南民族学院学报（自然科学版）》
2001年第3期304-308,312,共6页
Journal of Southwest Nationalities College(Natural Science Edition)
