摘要
针对一类非线性色散耗散波动方程研究了双线性元逼近.基于该元的高精度分析和插值后处理技巧,对于半离散格式,在精确解的合理正则性假设下得到了H^11模意义下最优误差估计及超逼近性和超收敛结果.同时,通过构造一个新的外推格式,导出了具有三阶精度的外推解.最后,建立了一个全离散逼近格式及研究其解的超逼近性.
The bilinear element approximation is discussed for a class of nonlinear dispersiondissipative wave equations. Based on the high acuraccy analysis of the element and interpolation post-processing technique, the optimal order error estimate, superclose property and superconvergence result in H1 norm are deduced for semi-discrete scheme under the proper regularity property hypothesis of the exact solution. At the same time, the extrapolation result with three order is obtained by constructing a new extrapolation scheme. Finally, a fully-discrete scheme is established and the superclose property is studied.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2014年第6期1599-1610,共12页
Acta Mathematica Scientia
基金
国家自然科学基金(10971203
11271340)
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)资助
关键词
非线性色散耗散波动方程
超收敛和外推
双线性元
半离散和全离散格式
Nonlinear dispersion-dissipative wave equations
Superconvergence and extrapolation
Bilinear element
Semi-discrete and fully-discrete schemes.