一类具有强阻尼Sine-Gordon方程异性网格上的超收敛分析
Superconvergence Analysis for a Class of Sine-Gordon Equations with Strong Damping on Anisotropic Meshes

作者: 乔保民 :商丘师范学院数学与信息科学学院;

关键词: 各向异性网格Sine-Gordon方程强阻尼双二次元误差估计超收敛 Anisotropic Meshes Sine-Gordon Equations Strong Damping Parabolic Element Error Estimate Superconvergence

摘要:
在异性网格下,利用双二次有限元逼近对一类具有强阻尼Sine-Gordon方程半离散格式进行了收敛性分析。同时,利用插值算子与Ritz投影相一致的性质给出了超逼近性质。最后,通过使用插值后处理技巧得到了它的整体超收敛结果。

Abstract:
The aim of this paper is to study the convergence analysis for a class of Sine-Gordon equations with strong damping by parabolic element under anisotropic meshes. Result of superclose about the nerve transmission signal can be acquired by virtue of the property that the interpolated operator is accordance with the Ritz projection. Finally, the corresponding global superconvergence is got by taking the advantage of the technique of the post-processing operator.

文章引用: 乔保民 (2013) 一类具有强阻尼Sine-Gordon方程异性网格上的超收敛分析。 理论数学, 3, 234-239. doi: 10.12677/PM.2013.33035

参考文献

[1] 张建文, 王旦霞等. 一类广义强阻尼Sine-Gordon方程的整体解[J]. 物理学报, 2008, 57(4): 2021-2025.

[2] 周盛凡. 有阻尼Sine-Gordon方程的全局吸引子的维数[J]. 数学学报, 1996, 39(5): 597-601.

[3] 李全国. 非齐次边界条件下Sine-Gordon型二阶非线性系统的全局吸引子及能稳性[J]. 应用数学学报, 2006, 29(6): 1119-1124.

[4] Z. Q. Liang. The global solution and numerical computation of the generalized nonlinear Sine-Gordon equation. Mathematics Applicate, 2003, 16(4): 40-49.

[5] 许秋滨, 张路明. 二维有阻尼方程的一个交替方向隐格式[J]. 应用数学学报, 2007, 30(5): 1111-1114.

[6] V. Thomee, J. C. Xu and N. Y. Zhang. Superconvergence of the gradient in piecewise linear finite element approximation to a parabolic problem. SIAM Journal on Numerical Analysis, 1989, 26: 553-573.

[7] Q. Lin, J. H. Pan. superconvergence for biquadratic elements in parabolic problem. Hong Kong: Hong Kong Great Wall Culture Publish Co., 1991: 217-229.

[8] 石东洋, 龚伟. 各向异性网格上抛物方程全离散格式的高精度分析[J]. 数学物理学报, 2009, 29A(4): 898-911.

[9] D. Y. Shi, S. P. Mao and H. Liang. Anisotropic biquadratic finite with superclose results. Journal of Systems Science and Complexity, 2006, 19(4): 566-576.

[10] 石东洋, 任金城等. Sobolev型方程各向异性下Wilson元的高精度分析[J]. 高等学校计算数学学报, 2009, 31(2): 169-171.

[11] 石东洋, 张熠然. 非定常Stokes问题的矩形Crouzeix-Rawiart型各向异性非协调元变网格方法[J]. 数学物理学报, 2006, 26A(5): 659- 670.

[12] D. Y. Shi, S. P. Mao and S. C. Chen. An anisotropic nonconforming finite with some superconvergence results. Journal of Computational May- hematics, 2005, 23(3): 261-274, 280.

[13] 石东洋, 谢丽萍, 陈绍春. 双曲积分微分方程的各向异性非协调有限元逼近[J]. 应用数学学报, 2007, 30(4): 1-13.

[14] 石东洋, 谢萍丽. Sobolev方程的一类各向异性非协调有限元逼近 [J]. 系统科学与数学, 2009, 29(1): 116-128.

[15] 石东洋, 高新慧. 抛物问题各向异性有限元的超收敛分析[J]. 应用数学, 2007, 20(4): 27-33.

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