A BALANCED OVERSAMPLING FINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS WITH OBSERVATIONAL BOUNDARY DATA  

作　　者：Zhiming Chen Rui Tuo Wenlong Zhang 

机构地区：[1]LSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Science,University of Chinese Academy of Sciences,Beijing 1000&9,China [3]Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [4]Department of Industrial&Systems Engineering,Texas 4&M University,College Station,TX 77843,USA [5]School of Mathematical Science,University of Chinese Academy of Sciences,Beijing 100190,China [6]Department of Mathematics,Southern University of Science and Technology,Shenzhen 518055,China

出　　处：《Journal of Computational Mathematics》2020年第2期355-374,共20页计算数学（英文）

基　　金：This work was supported in part by the National Center for Mathematics and Interdisciplinary Sciences,CAS and China NSF under the grant 118311061 and 11501551.

摘　　要：In this paper we propose a finite element method for solving elliptic equations with observational Dirichlet boundary data which may subject to random noises.The method is based on the weak formulation of Lagrangian multiplier and requires balanced oversampling of the measurements of the boundary data to control the random noises.We show the convergence of the random finite elemen t error in expec tat ion and,when the noise is subGaussian,in the Orlicz^2-norm which implies the probability that the finite element error estimates are viola ted decays exponentially.Numerical examples are included.

关 键 词：Observational boundary data Elliptic equation Sub-Gaussian random variable. 

分 类 号：O241.82[理学—计算数学]