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Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction

Published online by Cambridge University Press:  03 June 2015

Mingxia Li,
Jingzhi Li and
Shipeng Mao
Mingxia Li*
Affiliation:
School of Science, China University of Geosciences (Beijing), Beijing 100083, China
Jingzhi Li*
Affiliation:
Faculty of Science, South University of Science and Technology of China, Shenzhen 518055, China
Shipeng Mao*
Affiliation:
LSEC, Institute of Computational Mathematics, AMSS, Chinese Academy of Sciences (CAS), Beijing 100190, China
*
Email:limx@lsec.cc.ac.cn
Corresponding author.Email:li.jz@sustc.edu.cn
Email:maosp@lsec.cc.ac.cn
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Abstract

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.

Keywords

65N2165N5065N30Inverse problemsadaptive finite element methoda posteriori error estimatesquasi-orthogonalityconvergence analysis

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 4 , April 2014, pp. 1068 - 1090
Copyright
Copyright © Global Science Press Limited 2014

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