非线性对流扩散方程的隐-显hp-局部间断Galerkin有限元方法被引量：2

Implicit-explicit hp-local discontinuous Galerkin finite element method for nonlinear convection diffusion problems

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摘要使用Arnold等人提出的求解椭圆方程的间断有限元的一般框架及新的处理非线性对流项的方法,得到了非线性对流扩散方程的全离散隐-显hp-LDG方法的误差估计.对粘性Burgers方程进行了数值计算,计算结果验证了文中得到的理论结果并表明隐-显hp-LDG格式可使用比显式hp-LDG格式更大的时间步长. By using the general framework introduced by Arnod et al. and the new method dealting with the nonlinear convection term, the error estimates of implicit-explicit hp-LDG method for nonlinear convection diffusion problems are obtained. The numerical example for the nonlinear Burgers equation is presented in the paper. The numerical results verify the theoretical results obtained in this paper and demonstrate that implicit-explicit hp-LDG scheme can use much larger time step than explicit hp-LDG scheme.

作者由同顺

机构地区南开大学数学科学学院

出处《高校应用数学学报（A辑）》 CSCD 北大核心 2013年第4期447-456,共10页 Applied Mathematics A Journal of Chinese Universities(Ser.A)

关键词对流占优扩散方程隐-显hp-LDG方法提升算子误差估计 convection diffusion equation implicit-explicit hp-LDG method lifting operator error estimates

分类号 O241.8 [理学—计算数学]

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参考文献12

1Arnold D N, Brezzi F, Cockburn B, et al. Unified analysis of discontinuous Galerkin methods for elliptic problems[J]. SIAM J Numer Anal, 2001, 39: 1749-1779.
2Cockburn B, Karniadakis G, Shu C W. Discontinuous Galerkin Methods. Theroy, Computation and Applications[A]. Lecture Notes in Computational Science and Engineering, Vol. 11 [C]. Berlin: Springer Verlag, 2000.
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4Cockburn B, Shu C W. The local discontinuous Galerkin method for time-dependent convection-diffusion systerms[J]. SIAM J Numer Anal, 1998, 35: 2440-2463.
5由同顺.非线性对流扩散问题的hp-局部间断Galerkin有限元方法[J].工程数学学报,2012,29(6):894-906. 被引量：4
6Perugia I, Schotzau D. An hp-analysis of the local discontinuous Galerkin method for diffusion problems[J]. J Sci Comput, 2002, 17: 561-571.
7Perugia I, Schotzau D. The hp-Iocal discontinuous Galerkin method for low-frequency timeharmonic Maxwell equations[J]. Math Comp, 2003, 72: 1179-1214.
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10Brezzi F, Manzini G, Marini D, et al. Discontinuous Galerkin approximations for elliptic problems[J]. Numer Methods for Partial Differential Equations, 2000, 16: 365-378.

二级参考文献22

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5Cockburn B, Shu C W. Runge-Kutta discontinuous Galerkin methods for convection-dominated prob- lems[J]. Journal of Scientific Computing, 2001, 16(3): 173-261.
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8Castillo P, et al. Optimal a priori error estimates for the hp-version of convection-diffusion problems[J]. Mathematics of Computation, 2002, 71(238): 455-478.
9Perugia I, Sch6tzau D. The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations[J]. Mathematics of Computation, 2003, 72(243): 1179-1214.
10Perugia I, SchStzau D. An hp-analysis of the local discontinuous Galerkin method for diffusion problems[J]. Journal of Scientific Computing, 2002, 17(1-4): 561-571.