PM  >> Vol. 1 No. 2 (July 2011)

    耦合非线性抛物方程组的H1-Galerkin混合元方法
    H1-Galerkin Mixed Element Method for the Coupling Nonlinear Parabolic Partial Equations

  • 全文下载: PDF(893KB) HTML    PP.73-79   DOI: 10.12677/pm.2011.12016  
  • 下载量: 3,296  浏览量: 11,263   国家自然科学基金支持

作者:  

王金凤:内蒙古财经学院统计与数学学院,呼和浩特;
刘洋,李宏:内蒙古大学数学科学学院,呼和浩特;
李晓瑜:内蒙古工业大学理学院,呼和浩特

关键词:
耦合非线性抛物方程组H1-Galerkin混合元方法向后欧拉方法最优阶误差估计
Coupling Nonlinear Parabolic Partial Equations;H1-Galerkin Mixed Element Method; Backward Euler’s Method; Optimal Error Estimates

摘要:

利用H1-Galerkin混合有限元方法讨论耦合非线性抛物方程组,得到一维情形的半离散和全离散格式和未知存量函数和它的梯度的最优收敛阶误差估计,而且不用验证LBB相容性条件。最后,通过数值例子验证了该算法的可行性。

An H1-Galerkin mixed finite element method is discussed for the coupling nonlinear parabolic partial equations. Semidiscrete and fully discrete schemes and optimal error estimates of the scalar unknown and its gradient are derived for problems in one space dimension, and it dose not require the LBB consistency condition. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

文章引用:
王金凤, 刘洋, 李宏, 李晓瑜. 耦合非线性抛物方程组的H1-Galerkin混合元方法[J]. 理论数学, 2011, 1(2): 73-79. http://dx.doi.org/10.12677/pm.2011.12016

参考文献

[1] Z. D. Luo, R. X. Liu. Mixed finite element analysis and numerical solitary solution for the RLW equation. SIAM Journal on Numerical Analysis, 1998, 36(1): 89-104.
[2] Y. P. Chen, Y. Q. Huang. The superconvergence of mixed finite element methods for nonlinear hyperbolic equations. Communications in Nonlinear Science and Numerical Simulation, 1998, 3(3): 155-158.
[3] A. K. Pani. An H1-Galerkin mixed finite element method for parabolic partial differential equations. SIAM Journal on Numerical Analysis, 1998, 35(2): 712-727.
[4] A. K. Pani, G. Fairweather. H1-Galerkin mixed finite element methods for parabolic partial integro-differential equations. IMA Journal of Numerical Analysis, 2002, 22(2): 231-252.
[5] D. Y. Shi, H. H. Wang. An H1-Galerkin nonconforming mixed finite element method for integro-differential equation of parabolic type. Journal of Mathematical Research and Exposition, 2009, 29(5): 871-881.
[6] 王瑞文. 双曲型积分微分方程的H1-Galerkin混合有限元方法误差估计[J]. 计算数学, 2006, 28(1): 19-30.
[7] A. K. Pani, R. K. Sinha, and A. K. Otta. An H1-Galerkin mixed method for second order hyperbolic equations. International Journal of Numerical Analysis and Modeling, 2004, 1(2): 111-129.
[8] Y. Liu, H. Li. H1-Galerkin mixed finite element methods for pseudo-hyperbolic equations. Applied Mathematics and Computation, 2009, 212(2): 446-457.
[9] 郭玲, 陈焕贞. Sobolev方程的H1-Galerkin混合有限元方法[J]. 系统科学与数学, 2006, 26(3): 301-314.
[10] M. F. Wheeler. A priori L2-error estimates for Galerkin approximations to parabolic differential equation. SIAM Journal on Numerical Analysis, 1973, 10(4): 723-749.