Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction

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.