(untitled) (Communications in Computational Physics, 2020)
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.