四川师范大学学报（自然科学版）2012，Vol.35Issue(5)：610-614,5.DOI:10.3969/j.issn.1001-8395.2012.05.008
一类非线性广义Sine-Gordon方程的有限元超收敛分析
Superconvergence Analysis of a Finite Element to a Class of Generalized Nonlinear Sine-Gordon Equations
摘要
Abstract
Sine-Gordon equations play an important role in many important mathematical physics problems. There are many results about their numerical solutions which are obtained under traditional regular meshes. In this paper, the generalized nonlinear Sine-Gor-don equations are discussed by using bilinear finite element under anisotropie meshes. Firstly, the same convergence result as tradition-al one under regular meshes about these equations solution is obtained. Secondly, the superapproximation of the solution u is obtained by virtue of the interpolation operator but Ritz projection. Finally, based on the interpolated postprocessing technique, the global super-convergence is derived.关键词
非线性Sine - Gordon方程/双线性有限元/各向异性/半离散/超收敛Key words
generalized nonlinear Sine-Gordon equations/ bilinear finite element/ anisotropie/ semidiscretization/ superconver-gence分类
数理科学引用本文复制引用
梁洪亮,赵树理..一类非线性广义Sine-Gordon方程的有限元超收敛分析[J].四川师范大学学报（自然科学版）,2012,35(5):610-614,5.基金项目
国家自然科学基金(10971203)、河南省自然科学基金(092300410148)和河南省教育厅自然科学基金(2011A110013)资助项目 （10971203）
