线性对流占优扩散问题的修正特征混合有限元方法  

Modified Characteristics-mixed Finite Element Method with Adjusted Advection for the Linear Convection-dominated Diffusion Problems

作　　者：刘中艳[1] 陈焕贞[1] 

机构地区：[1]山东师范大学数学科学学院,济南250014

出　　处：《工程数学学报》2009年第2期200-208,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10271068);山东省自然科学基金(Z2006A02);山东省优秀中青年科学家科研奖励基金(2004BS01009)

摘　　要：本文对一类线性对流占优扩散问题提出了一种修正的特征混合有限元格式,该格式对方程的对流部分沿流体流动的方向即特征方向离散以保证格式在流动的锋线前沿逼近的高稳定性,消除数值弥散现象;对方程的扩散部分采用最低次混合有限元方法离散以同时高精度逼近未知函数及未知函数的梯度;为保证方法的整体守恒性,在格式中引入—修正项。数值分析表明,文中提出的修正的特征混合有限元方法具有所期望的稳定性,收敛性及整体守恒性。In this paper, we use the modified characteristics-mixed finite element method with adjusted advection to simulate the linear convection-dominated diffusion problems. The method is a combination of characteristic approximation to handle the convection part along the direction of fluid, namely characteristic direction, to ensure the high stability of the method in approximating the sharp fronts and to reduce the numerical diffusion, and a mixed finite element spatial approximation to deal with diffusion part, the unknown scalar and the adjoint vector function are approximated optimally and simultaneously. Especially, the characteristics line direction is slightly adjusted in order to preserve the integral conservation of the method. Numerical analysis indicates that the modified characteristicmixed finite element method has the desired stability, convergence and integral conservation.

关 键 词：对流占优扩散问题 修正的特征混合有限元方法 最优误差估计 

分 类 号：O241.8[理学—计算数学]