电报方程的一个最低阶新混合元格式逼近  

A new lowest order mixed finite element scheme approximation for telegraph equations

作　　者：李永献 曹欣杰[2] LI Yongxian;CAO Xinjie(School of Mathematics and Physics, Henan University of Urban Construction, Pingdingshan 467036, China;School of Mathematics and Informatics, Pingdingshan University, Pingdingshan 467000, China)

机构地区：[1]河南城建学院数理学院,河南平顶山467036 [2]平顶山学院数学与信息科学学院,河南平顶山467000

出　　处：《安徽大学学报（自然科学版）》2021年第2期17-22,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11271340);河南省高等学校重点科研项目(16B110002);河南城建学院科研基金资助项目(2015JZD007,2016QY018)。

摘　　要：针对电报方程构造一个新的最低阶三角形协调混合元格式,证明了该格式解的存在唯一性.在抛弃传统有限元分析中不可或缺的Ritz投影的情况下,利用积分恒等式和平均值技巧,在半离散情形下分别导出了原始变量在H1模及流量在L2模意义下的超逼近性质.借助新构造的插值后处理算子,得到了相应的整体超收敛结果.A new lowest order triangular conforming mixed finite element formulation was proposed for telegraph equations,and the existence and uniqueness of the above pattern were proved.With the help of the integral identity and mean-value technique,the superclose properties for the primitive solution in H1-norm and the flux in L2-norm for semi-discrete scheme were obtained without requiring the Ritz projection operator which was indispensable in traditional finite element analysis,respectively.Furthermore,by employing a new constructed interpolated postprocessing approach,the corresponding superconvergence results were deduced.

关 键 词：电报方程 混合元新格式 三角形元 超逼近 超收敛 

分 类 号：O242.21[理学—计算数学]