A Symmetric Characteristic Finite Volume Element Scheme for Nonlinear Convection-Diffusion Problems  

作　　者：Min Yang Yi-rang Yuan 

机构地区：[1]Department of Mathematics, Yantai University, Yantai, 264005 China [2]School of Mathematical and System Science, Shandong University, Jinan 250100, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第1期41-54,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No. 10372052,10271066) ;the Doctorate Foundation of the Ministry of Education of China (Grant No.20030422047).

摘　　要：In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems. Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O（△t2 ＋ h） and present some numerical examples at the end of the paper.In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems. Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O（△t2 ＋ h） and present some numerical examples at the end of the paper.

关 键 词：Finite volume element symmetric scheme NONLINEAR alternating direction error estimates 

分 类 号：O175[理学—数学]