非定常线性对流扩散问题的算子分裂半显式有限元分析  

ANALYSIS OF OPERATOR SPLITTING SEMI-EXPLICIT FINITE ELEMENT METHOD FOR TIME-DEPENDENT LINEAR CONVECTIVE-DIFFUSION PROBLEMS

作　　者：孙澈[1] 秦树杰[1] 

机构地区：[1]南开大学数学系,天津300071

出　　处：《计算数学》2003年第1期23-34,共12页Mathematica Numerica Sinica

基　　金：国家科学基金资助项目(19771050与10171052)

摘　　要：1.引言 在现代科学及工程领域中,存在着许多同时伴有物质传输和动力耗散两种过程的物理系统.在数学上,它们常归结为对流占优的对流扩散方程或以这种方程占主导的方程组.这类方程具有殆双曲性质,其解函数常呈现局部大梯度变化,使得传统的求解抛物问题的数值方法常常失效.In this paper, a convective-diffusion problem is splitted into two simple problems-frist-order hyperbolic problem and heat-conductive problem by operator-splitting method. A coupling scheme consisted by a full discrete discontinuous finite element method with a full discrete Galerkin method is constructed. For this scheme,the stability is proved and the optimal L2(H1) order and quasi-optimal L∞(L2) order error estimate is established.

关 键 词：对流扩散 算子分裂-有限元方法 显式有限元 对流占优 双曲问题 热传导问题 线性问题 

分 类 号：O241.82[理学—计算数学] O175.27[理学—数学]