二维Burgers方程的RKDG有限元解法  

The RKDG Finite Element Method for Burgers Equation

作　　者：马艳春[1] 张寅虎[2] 冯新龙[1] 

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046 [2]咸阳师范学院数学系,咸阳712000

出　　处：《工程数学学报》2013年第3期442-450,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61163027;10901131);新疆科技厅特培基金(201123117);新疆大学自然科学基金(XY080102)~~

摘　　要：本文应用RKDG有限元方法求解具有周期边界条件的二维非粘性Burgers方程,并给出稳定性分析和误差估计.基于一致网格剖分,采用Q1矩形元和广义斜率限制器进行数值模拟.在相同网格剖分下与三角元相比,矩形元剖分的自由度较少,计算复杂度低,易于实现.In this paper, the Runge-Kutta discontinuous Galerkin finite element method is pre- sented for solving two-dimensional inviscid Burgers equation with periodic boundary condition. Stability analysis and error estimates are derived, respectively. Based on the uniform mesh, the generalized slope limiter and the Q^1 rectangular element are used in numerical experiments. Compared with the triangular element, the rectangular element needs less degree of freedom. And it is easy to implement and extend to high dimensional problems.

关 键 词：BURGERS方程 RKDG有限元方法 矩形元 数值通量 

分 类 号：O241.82[理学—计算数学]