Sobolev方程的混合连续时空有限元解的误差估计  

Error Estimates of Mixed Space-Time Finite Element Solutions to Sobolev Equations

作　　者：庞乃虹 李宏 PANG Naihong;LI Hong(School of Mathematical Sciences,Inner Mongolia University,Huhhot 010021,P.R.China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《应用数学和力学》2020年第8期834-843,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11761053);内蒙古自然科学基金(2017MS0107);内蒙古自治区草原英才工程;内蒙古自治区青年科技英才支持计划(NJYT-17-A07)。

摘　　要：通过引入辅助变量构造Sobolev方程的混合连续时空有限元离散格式,使得该格式既利用混合法将方程降阶,又将时间和空间两个变量同时用有限元方法离散,从而获得时空形式高精度数值模型.证明了Sobolev方程混合时空有限元解的存在唯一性、稳定性,并利用时间和空间投影算子推导出时空数值解的误差估计.The mixed space-time finite element scheme for Sobolev equations was constructed through introduction of auxiliary variables.The scheme can not only reduce the order of the equation with the mixed method,but discretize both space and time variables by means of the finite element technique.A numerical model of high-order accuracy in space and time was obtained.The existence,stability and uniqueness of the mixed space-time finite element solution were proved.The error estimates were derived with the space-time projection operator.

关 键 词：混合法 时空有限元格式 SOBOLEV方程 存在唯一性、稳定性 误差估计 

分 类 号：O241.82[理学—计算数学]