非线性sine-Gordon方程的各向异性线性元高精度分析新模式  

A NEW PATTERN OF HIGH ACCURACY ANALYSIS OF ANISOTROPIC LINEAR ELEMENT FOR NONLINEAR SINE-GORDON EQUATIONS

作　　者：石东洋[1] 王芬玲[2] 赵艳敏[2,1] 

机构地区：[1]郑州大学数学与统计学院,郑州450001 [2]许昌学院数学与统计学院,河南许昌461000

出　　处：《计算数学》2014年第3期245-256,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10971203;11271340;11101381);高等学校博士学科点专项科研基金(20094101110006);河南省教育厅资助基金(14A110009)

摘　　要：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.A new pattern of high accuracy analysis of linear triangular element is proposed for a kind of nonlinear sine-Gordon equations on anisotropic meshes. Based on integral indentity result of this element, an error estimate is derived between the interpolation and Riesz projection. By use of the interpolated post-processing technique, superclose and superconvergence results are obtained in semi-discrete and fully-discrete schemes, which can＇t be deduced by the interpolation or Riesz projection alone. Finally, some popular finite elements are investigated.

关 键 词：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 

分 类 号：O241.82[理学—计算数学]