Mixed Time Discontinuous Space-Time Finite Element Method for Convection Diffusion Equations
-
摘要: 构造并分析二阶对流扩散方程的混合时间间断时空有限元格式.利用混合有限元方法将二阶方程降阶,利用空间连续而时间允许间断的时空有限元方法离散低阶方程.证明数值解的稳定性、存在唯一性和收敛性.最后通过数值结果验证该算法的有效性和可行性.
-
关键词:
- 对流扩散方程 /
- 混合有限元法 /
- 时间间断时空有限元法 /
- 收敛性
Abstract: A mixed time discontinuous space-time finite element scheme for second order convection diffusion problems is constructed and analyzed.The order of the equation was lowered by mixed finite element method. And the low order equation was discretized by space-time finite element method,continuous in space but discontinuous in time.The stability,existence,uniqueness and convergence of the approximate solutions were proved.Finally,numerical results were presented to illustrate the efficiency of the method. -
[1] Reed N H, Hill T R.Triangle mesh methods for the Neutron transport equation[R]. Los Alamos Scientific Laboratory,Report LA2 UR-73-479,1973. [2] Cockburn B,Lin S Y.TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws Ⅲ: one-dimensional systems[J].J Comp Phys,1989,84(1):90-113. doi: 10.1016/0021-9991(89)90183-6 [3] Cockburn B,Hou S C,Shu C W. TVB Runge-Kutta local projection discontinuous Galerkin method for conservation laws Ⅳ: the multidimensional case[J].J Comp Phys,1990,54(3):545-581. [4] Thomée Vider.Galerkin Finite Element Methods for Parabolic Problems[M].New York:Springer-Verlag,1997. [5] 李宏,郭彦. 四阶抛物方程的间断时空混合有限元法[J].内蒙古大学学报(自然科学版),2006,37(1):20-22. [6] Brezzi F,Hughes T J R,Marini L D,et al.Mixed discontinuous galerkin methods for darcy flow[J].Journal of Scientific Computing,2005,22(2):119-145. doi: 10.1007/s10915-004-4150-8 [7] 李宏,刘儒勋. 抛物方程的时空有限元方法[J].应用数学和力学,2001,22(6):613-624. [8] 汤琼,陈传淼,刘罗华.Schrdinger方程的时空有限元方法与守恒性[J].应用数学和力学,2006,27(3):300-304. [9] CHEN Zhang-xin.Finite Element Methods and Their Applications[M].Berlin Heidelgerg:Springer-Verlag,2005. [10] YAN Jue,SHU Chi-wang.A Local discontinuous galerkin method for KdV-type equation[R]. NASA/CR-2001-211026 ICASE Report No. 2001-20.
计量
- 文章访问数: 3093
- HTML全文浏览量: 187
- PDF下载量: 539
- 被引次数: 0