Convergence analysis of an adaptive finite element method for distributed flux reconstruction
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 algorithm. Show more
Publication status
unpublishedJournal / series
Research ReportVolume
Publisher
ETH Zürich, Seminar für Angewandte MathematikSubject
Inverse problems; Adaptive finite element method; A posteriori error estimates; Quasiorthogonality; Convergence analysisOrganisational unit
03632 - Hiptmair, Ralf / Hiptmair, Ralf
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