Volume 31, Issue 4
A Priori Error Estimates of a Finite Element Method for Distributed Flux Reconstruction

J. Comp. Math., 31 (2013), pp. 382-397.

Published online: 2013-08

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• Abstract

This paper is concerned with a priori error estimates of a finite element method for numerical reconstruction of some unknown distributed flux in an inverse heat conduction problem. More precisely, some unknown distributed Neumann data are to be recovered on the interior inaccessible boundary using Dirichlet measurement data on the outer accessible boundary. The main contribution in this work is to establish the a priori error estimates in terms of the mesh size in the domain and on the accessible/inaccessible boundaries, respectively, for both the temperature $u$ and the adjoint state $p$ under the lowest regularity assumption. It is revealed that the lower bounds of the convergence rates depend on the geometry of the domain. These a priori error estimates are of immense interest by themselves and pave the way for proving the convergence analysis of adaptive techniques applied to a general class of inverse heat conduction problems. Numerical experiments are presented to verify our theoretical prediction.

• Keywords

Distributed flux, Inverse heat problems, Finite element method, Error estimates.

35R30, 65N30, 65N15.

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@Article{JCM-31-382, author = {}, title = {A Priori Error Estimates of a Finite Element Method for Distributed Flux Reconstruction}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {4}, pages = {382--397}, abstract = {

This paper is concerned with a priori error estimates of a finite element method for numerical reconstruction of some unknown distributed flux in an inverse heat conduction problem. More precisely, some unknown distributed Neumann data are to be recovered on the interior inaccessible boundary using Dirichlet measurement data on the outer accessible boundary. The main contribution in this work is to establish the a priori error estimates in terms of the mesh size in the domain and on the accessible/inaccessible boundaries, respectively, for both the temperature $u$ and the adjoint state $p$ under the lowest regularity assumption. It is revealed that the lower bounds of the convergence rates depend on the geometry of the domain. These a priori error estimates are of immense interest by themselves and pave the way for proving the convergence analysis of adaptive techniques applied to a general class of inverse heat conduction problems. Numerical experiments are presented to verify our theoretical prediction.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1304-m4024}, url = {http://global-sci.org/intro/article_detail/jcm/9742.html} }
TY - JOUR T1 - A Priori Error Estimates of a Finite Element Method for Distributed Flux Reconstruction JO - Journal of Computational Mathematics VL - 4 SP - 382 EP - 397 PY - 2013 DA - 2013/08 SN - 31 DO - http://doi.org/10.4208/jcm.1304-m4024 UR - https://global-sci.org/intro/article_detail/jcm/9742.html KW - Distributed flux, Inverse heat problems, Finite element method, Error estimates. AB -

This paper is concerned with a priori error estimates of a finite element method for numerical reconstruction of some unknown distributed flux in an inverse heat conduction problem. More precisely, some unknown distributed Neumann data are to be recovered on the interior inaccessible boundary using Dirichlet measurement data on the outer accessible boundary. The main contribution in this work is to establish the a priori error estimates in terms of the mesh size in the domain and on the accessible/inaccessible boundaries, respectively, for both the temperature $u$ and the adjoint state $p$ under the lowest regularity assumption. It is revealed that the lower bounds of the convergence rates depend on the geometry of the domain. These a priori error estimates are of immense interest by themselves and pave the way for proving the convergence analysis of adaptive techniques applied to a general class of inverse heat conduction problems. Numerical experiments are presented to verify our theoretical prediction.

Mingxia Li, Jingzhi Li & Shipeng Mao. (1970). A Priori Error Estimates of a Finite Element Method for Distributed Flux Reconstruction. Journal of Computational Mathematics. 31 (4). 382-397. doi:10.4208/jcm.1304-m4024
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