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Convergence analysis of an adaptive finite element method for distributed flux reconstruction

by J. Li and M. Li and S. Mao

(Report number 2011-62)

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.

Keywords: Inverse problems, adaptive finite element method, a posteriori error estimates, quasiorthogonality, convergence analysis

@Techreport{LLM11_126,
  author = {J. Li and M. Li and S. Mao},
  title = {Convergence analysis of an adaptive finite element method for distributed flux reconstruction},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-62},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-62.pdf },
  year = {2011}
}

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