Convergence and error analysis of a numerical method for the identification of matrix parameters in elliptic PDEs

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Erscheinungsjahr:
2012
Medientyp:
Text
Schlagworte:
  • Inverse problem
  • Parameter identification
  • Parabolic equation
  • Inverse Problems
  • Boundary Value Problems
  • Heat Conduction
  • Inverse problem
  • Parameter identification
  • Parabolic equation
  • Inverse Problems
  • Boundary Value Problems
  • Heat Conduction
Beschreibung:
  • We analyze a numerical method for solving the inverse problem of identifying the diffusion matrix in an elliptic PDE from distributed noisy measurements. We use a regularized least-squares approach in which the state equations are given by a finite element discretization of the elliptic PDE. The unknown matrix parameters act as control variables and are handled with the help of variational discretization as introduced in (Hinze M 2005 Comput. Optim. Appl. 30 45-61). For a suitable coupling of Tikhonov regularization parameter, finite element grid size and noise level we are able to prove L 2-convergence of the discrete solutions to the unique norm-minimal solution of the identification problem; corresponding convergence rates can be obtained provided that a suitable projected source condition is fulfilled. Finally, we present a numerical experiment which supports our theoretical findings. © 2012 IOP Publishing Ltd.
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  • info:eu-repo/semantics/restrictedAccess
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Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/20acc21d-6bb6-4dc4-b630-d48a3b294902