@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} }