二维非线性对流扩散方程特征有限元方法  

Characteristic finite element method for 2-D nonlinear convection-diffusion problems

作　　者：张引娣[1] 封建湖[1] 余剑生[1] 

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《长安大学学报（自然科学版）》2010年第3期105-110,共6页Journal of Chang’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(10971165)

摘　　要：应用特征有限元Galerkin方法,研究对流占优的二维非线性对流-扩散方程的数值求解问题。建立了非线性对流-扩散方程的特征有限元Galerkin形式,给出了特征有限元法的最优阶误差估计。误差分析及数值结果表明,该方法具有较好的收敛性与稳定性,并且克服了用有限元或差分法经常出现的数值振荡现象。Applying characteristic finite element Galerkin method,a numerical solution was discussed for 2-D nonlinear convection-dominated diffusion problems.A characteristic finite element Galerkin scheme was established for 2-D nonlinear convection-dominated diffusion equation here.Two optimal error estimates of the scheme were given.The estimates analysis and numerical test show that,for 2-D nonlinear convection-dominated diffusion problems,the scheme here has the better convergence and stability than others,and avoids the oscillating with finite element or finite difference procedure.2 tabs,6 figs,10 refs.

关 键 词：对流扩散方程 特征有限元方法 误差估计 对流占优 SOBOLEV空间 

分 类 号：O241.82[理学—计算数学]