一维对流扩散方程第三边值问题的紧有限体积格式  

A compact finite volume scheme for one-dimensional convection diffusion equations with third boundary conditions

作　　者：陈宏霞[1] 王同科[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2013年第2期10-19,共10页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071123)

摘　　要：针对一维常系数对流扩散方程第三边值问题提出一种紧有限体积格式,该格式形成的线性代数方程组具有三对角性质,可以使用追赶法求解.用能量估计法证明了格式按照离散L2范数、H1半范数和最大模范数均具有4阶收敛精度.数值算例验证了理论分析的正确性,并说明了格式的有效性.A compact finite volume scheme is presented for one-dimensional convection diffusion equations with third boundary conditions with constant coefficients. The linear algebraic system derived by this scheme has tridiagonal property and can be solved by Thomas method. It is proved that the given scheme is convergent with fourth-order accuracy with re- spect to discrete L2 norm, H1 semi-norm and maximum norm by energy method. Numerical examples verify the correctness of the theoretical analysis and also show the effectiveness of the scheme.

关 键 词：对流扩散方程第三边值问题 紧有限体积格式 误差估计 4阶精度 

分 类 号：O241.82[理学—计算数学]