Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction (Communications in Computational Physics, 2020)
This paper studies convergence analysis of an adaptive finite element algorithmfor numerical estimation of some unknown distributed flux in a stationaryheat conduction system, namely recovering the unknown Neumann data on interiorinaccessible boundary using Dirichlet measurement data on outer accessible boundary.Besides global upper and lower bounds established in [23], a posteriori local upperbounds and quasi-orthogonality results concerning the discretization errors of thestate and adjoint variables are derived. Convergence and quasi-optimality of the proposedadaptive algorithm are rigorously proved. Numerical results are presented toillustrate the quasi-optimality of the proposed adaptive method.