Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction
Year: 2014
Author: Mingxia Li, Jingzhi Li, Shipeng Mao
Communications in Computational Physics, Vol. 15 (2014), Iss. 4 : pp. 1068–1090
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.050313.210613s
Communications in Computational Physics, Vol. 15 (2014), Iss. 4 : pp. 1068–1090
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Author Details
Mingxia Li Email
Jingzhi Li Email
Shipeng Mao Email