Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction  

作　　者：Mingxia Li Jingzhi Li Shipeng Mao 

机构地区：[1]School of Science,China University of Geosciences(Beijing),Beijing 100083,China [2]Faculty of Science,South University of Science and Technology of China,Shenzhen 518055,China [3]LSEC,Institute of Computational Mathematics,AMSS,Chinese Academy of Sciences(CAS),Beijing 100190,China

出　　处：《Communications in Computational Physics》2014年第4期1068-1090,共23页计算物理通讯（英文）

基　　金：supported by the NSFC grant(No.11101386);the Fundamental Research Funds for the Central Universities of China;supported by the NSFC grants(No.11201453 and 91130022);supported by the NSFC grants(No.11101414 and 91130026).

摘　　要：This paper studies convergence analysis of an adaptive finite element algorithm for numerical estimation of some unknown distributed flux in a stationary heat conduction system,namely recovering the unknown Neumann data on interior inaccessible boundary using Dirichlet measurement data on outer accessible boundary.Besides global upper and lower bounds established in[23],a posteriori local upper bounds and quasi-orthogonality results concerning the discretization errors of the state and adjoint variables are derived.Convergence and quasi-optimality of the proposed adaptive algorithm are rigorously proved.Numerical results are presented to illustrate the quasi-optimality of the proposed adaptive method.

关 键 词：Inverse problems adaptive finite element method a posteriori error estimates quasiorthogonality convergence analysis 

分 类 号：O17[理学—数学]