强阻尼波动方程的非协调有限元超收敛分析  

Superconvergence analysis of a nonconforming finite element for strongly damped wave equations

作　　者：张亚东[1] 李新祥[2] 石东洋[3] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]上海大学理学院,上海200444 [3]郑州大学数学与统计学院,河南郑州450001

出　　处：《山东大学学报（理学版）》2014年第5期28-35,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10971203;11271340;11101381);高等学校博士学科点专项科研基金(2009410111006)

摘　　要：研究了强阻尼波动方程的非协调有限元方法的超收敛性。在抛弃传统有限元分析中的必要工具-Ritz投影算子的前提下,直接利用单元的插值性质,在半离散和全离散格式下,得到了u在H1-模下的最优阶误差估计和超逼近性。借助于插值后处理技巧,得到了整体超收敛。给出了一些数值结果验证了理论分析的正确性。The superconvergence analysis of nonconforming finite element method for strongly damped wave equation is studied. The corresponding optimal order convergence error estimates and superclose property are obtained in broken H 1-norm for both semi-discrete and fully-discrete schemes based on the interpolation of the element directly instead of the Ritz projection operator,which is an indispensabel tool in the traditional finite element analyis. The global supercon-vergence is derived through interpolation post-processing technique. Finally,some numerical results are provided to show the validity of the theoretical analysis.

关 键 词：强阻尼波动方程 非协调有限元 半离散和全离散格式 超逼近 超收敛 

分 类 号：O242.21[理学—计算数学]