二维线性Sobolev方程广义差分法  

THE GENERALIZED DIFFERENCE SCHEME FOR LINEAR SOBOLEV EQUATION IN TWO DIMENSIONS

作　　者：曹艳华[1] 

机构地区：[1]首都师范大学数学系,北京100037

出　　处：《计算数学》2005年第3期243-256,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金(No.10471100;40437017)北京市自然科学基金资助项目.

摘　　要：本文考虑了二维线性Sobolev方程的一阶广义差分法.把Sobolev方程从一维区间推广到二维区域时会产生许多的问题.本文将证明其半离散广义差分解的存在唯一性,并且通过引入Ritz-Volterra投影给出其L^p模和W^(1,p)模误差估计.In this paper, the first order generalized difference scheme for linear Sobolev equation in two-dimension is considered. When the equation from one-dimension to two-dimension is populized, there will be many new problems. The existence and uniquenss of its semi-discrete generlized difference solutions are proved, and L^P and W^1,P-norm error estimates of u - Uh by means of the Ritz-Volterra projection u - Rh^u are given.

关 键 词：SOBOLEV方程 一阶广义差分法 误差估计 广义差分法 二维区域 线性 解的存在唯一性 模误差估计 半离散 区间 

分 类 号：O241.3[理学—计算数学]