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.