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Volume 15, Issue 4
Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction

Mingxia Li, Jingzhi Li & Shipeng Mao

DOI: 10.4208/cicp.050313.210613s

Commun. Comput. Phys., 15 (2014), pp. 1068-1090.

Published online: 2014-04

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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.

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@Article{CiCP-15-1068, author = {Mingxia Li, Jingzhi Li and Shipeng Mao}, title = {Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.050313.210613s}, url = {http://global-sci.org/intro/article_detail/cicp/7128.html} }
TY - JOUR T1 - Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction AU - Mingxia Li, Jingzhi Li & Shipeng Mao JO - Communications in Computational Physics VL - 4 SP - 1068 EP - 1090 PY - 2014 DA - 2014/04 SN - 15 DO - http://doi.org/10.4208/cicp.050313.210613s UR - https://global-sci.org/intro/article_detail/cicp/7128.html KW - AB -

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.

Mingxia Li, Jingzhi Li and Shipeng Mao. (2014). Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction. Communications in Computational Physics. 15 (4). 1068-1090. doi:10.4208/cicp.050313.210613s
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