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

Mingxia Li, Jingzhi Li & Shipeng Mao

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 = {}, 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 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 & Shipeng Mao. (2020). 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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