全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
计算数学  2014 

非线性sine-Gordon方程的各向异性线性元高精度分析新模式

, PP. 245-256

Keywords: sine-Gordon方程,超逼近和超收敛,线性三角形元,半离散和全离散格式

Full-Text   Cite this paper   Add to My Lib

Abstract:

在各向异性网格下,针对一类非线性sine-Gordon方程提出了线性三角形元新的高精度分析模式.基于该元的积分恒等式结果,导出了插值与Riesz投影之间的误差估计,再借助于插值后处理技术得到了在半离散和全离散格式下单独利用插值或Riesz投影所无法得到的超逼近和超收敛结果.最后,对一些常见的单元作了进一步探讨.

References

[1]  Liang Z Q. The global solution and numerical computation of the generalized noninear sine Gordon equation[J]. Math. Appl., 2003,16(4): 40-49.
[2]  Liu Y, Li H. Numerical solutions of H^1-Galerkin mixed finite element method for a damped sine-Gordon equation[J]. Math.Appl., 2009, 22(3): 579-588.
[3]  Wei G W. Discrete singular convolution for the sine-Gordon equation[J]. Physica D: Nonl. Phen., 2000, 137(3-4): 247-259.
[4]  蒋长锦. 二维非定常sine-Gordon方程辛算法及其孤子数值模拟[J].计算物理, 2003, 20(4): 321-325.
[5]  周盛凡.有阻尼sine-Gordon方程的全局吸引的维数[J]. 数学学报,1996, 39(5): 597-601.
[6]  许秋滨, 张鲁明. 二维广义非线性sine-Gordon方程的一个ADI格式[J]. 应用数学学报, 2007, 30(5): 836-846.
[7]  Zhang W, Wang X Y, Yao M H. Study on chaotic dynamics of perturbed sine-Gordon equation[J]. J. Beijing Univ. Tech., 2004,30(2): 134-138.
[8]  盛平兴. 广义sine-Gordon方程的混沌与湍流[J]. 应用数学学报,2005, 28(3): 836-846.
[9]  王芬玲, 石东洋. 非线性sine-Gordon方程Hermite型有限元新的超收敛分析及外推[J]. 应用数学学报, 2012, 35(5): 777-788.
[10]  石东洋, 张斐然. Sine-Gordon 方程的一类低阶非协调有限元分析[J]. 计算数学, 2011, 33(3): 289-297. 浏览
[11]  Shi D Y, Zhang D. Approximation of nonconforming quasi-Wilson element for sine-Gordon equation[J]. J. Comput. Math., 2013, 31(3): 271-282.
[12]  喻海元, 黄云清. 变系数情形下Criss-Cross三角形线性元的渐近展式与超收敛[J]. 计算数学, 2007, 29(3): 325-336. 浏览
[13]  陈传淼. 三角形线元与二次元L2投影的整体超收敛[J]. 计算数学,2003, 25(4): 385-392. 浏览
[14]  Vider Thomée. Galerkin Finite Element Methods for Parabolic Problems[M]. Spring-Verlag: Berlin Heidelberg, 1997.
[15]  Chen H T, Lin Q, Zhou J M, Wang H. Uniform error estimates for triangle finite element solutions of advection diffusion equations[J]. Adv. Comput. Math., 2013, 38(1): 83-100.
[16]  Lin Q, Wang H, Zhang S H. Uniform optimal-order estimates for finite element methods for advection-diffusion equations[J]. J. Syst. Sci. & Complexity, 2009, 22(4): 555-559.
[17]  林群, 王宏, 周俊明, 张书华, 陈宏焘. 对流扩散方程三角形有限元解的一致估计[J]. 数学的实践与认识, 2011, 41(21): 232-238.
[18]  陈宏焘, 林群, 周俊明. 对流扩散方程特征线三角形元法的一致估计[J]. 数学的实践与认识, 2011, 41(19): 173-184.
[19]  石东洋, 梁慧. 各向异性网格下线性三角形元的超收敛性分析[J]. 工程数学学报, 2007, 24(3): 487-493.
[20]  Shi Z C, Jiang B, Xue W M. A new superconvergence property of Wilson nonconforming finite element[J]. Numer. Math., 1997, 78(2): 259-268.
[21]  Shi D Y, Liang H. Superconvergence analysis Wilson element onanisotropic meshes[J]. Appl. Math. Mech., 2007, 28(1): 119-125
[22]  石东洋, 王芬玲, 史艳华. 各向异性EQ1rot非协调元高精度分析的一般格式[J]. 计算数学, 2013, 35(3): 239-252. 浏览
[23]  罗振东. 混合有限元法基础及其应用[M]. 科学出版社: 北京, 2006.
[24]  张铁. 偏微分-积分方程的有限元方法[M]. 科学出版社: 北京, 2009.
[25]  石东洋, 梁慧.一个新的非常规Hermite型各向异性矩形元的超收敛分析及外推[J]. 计算数学, 2005, 27(4): 369-382. 浏览
[26]  Lin Q, Tobiska L, Zhou A H. Superconvergence and extrapolation of nonconformimg low order finite elements applied to the Poisson equation[J]. IMA J. Numer. Anal., 2005, 25(1): 160-181.
[27]  Shi D Y, Mao S P, Chen S C. An anisotropic nonconforming finite element with some superconvergence results[J]. J. Comput. Math., 2005, 23(3): 261-274.
[28]  Shi D Y, Wang H H, Du Y P. An anisotropic nonconforming finite element method for approximating a class of nonlinear Sobolev equations[J]. J. Comput. Math., 2009, 27(2-3): 299-314.
[29]  Shi D Y, Zhou J Q, Shi D W. A new low order least squares nonconforming characteristics mixed finite element mathod for Burgers' equation[J]. Appl. Math. Comput., 2013, 219(24): 11302-11310.
[30]  Shi D Y, Yu Z Y. Low-order nonconforming mixed finite element methods for stationary incompressible magnetohydrodynamics equations[J].J. Appl. Math., 2013, 10(4): 904-919.
[31]  Rannacher R, Turek S. Simple nonconforming quadrilateral Stokes element[J]. Numer. Meth. PDEs, 1992, 8(2): 97-111.
[32]  胡俊, 满红英, 石钟慈. 带约束非协调旋转Q1元在Stokes和平面弹性问题的应用 [J]. 计算数学, 2005, 27(3): 311-324. 浏览
[33]  Park C J, Sheen D W. P1- nonconforming quadrilateral finite element method for second order elliptic problems[J]. SIAM J. Numer. Anal., 2003, 41(2): 624-640.
[34]  Shi D Y, Hao X B. Accuracy analysis for quasi-Carey element[J]. J. Syst. Sci. & Complexity, 2008, 21(3): 456-462.
[35]  Shi D Y, Xu C, Chen J H. Anisatropic nonconforming EQ1rot quadrilateral finite element approximation to second order elliptic problem[J].J. Sci. Comput., 2013, 56(3): 637-653.
[36]  Shi D Y, Xu C. EQ1rot nonconforming finite element approximation to Signorini problem[J]. Sci. China Math., 2013, 56(6): 1301-1311.
[37]  Chen S C, Shi D Y. Accuracy analysis for quasi-Wison element[J]. Acta Math. Sci., 2000, 20(1): 44-48.
[38]  Chen S C, Shi D Y. Zhao Y.C. Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes[J]. IMA J.Numer. Anal., 2004, 24(1): 77-95.
[39]  Shi D Y, Wang F L, Zhao Y M. Superconvergence analysis and extrapolation of quasi-Wilson nonconforming finite element method for nonlinear Sobolev equations[J]. Acta Math. Appl. Sin., 2013, 29(2): 403-414.
[40]  Shi D Y, Pei L F. Nonconforming quadrilateral finite element method for a class of nonlinear sine-Gordon equations[J]. Appl. Math. Comput., 2013, 219(17): 9447-9460.
[41]  Knobloch P,Tobiska L. The P1mod element: a new nonconforming finite element for convection-diffusion problems[J]. SIAM J. Numer. Anal., 2003, 41(2): 436-456.
[42]  石东洋,郝晓斌. Sobolev型方程各向异性Carey元的高精度分析[J].工程数学学报, 2009, 26(6): 1021-1026.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133