Numerical analysis of an energy-like minimization method to solve the Cauchy problem with noisy data

  • Authors:

  • R. Rischette;T. N. Baranger;N. Debit

  • Affiliations:

  • Université de Lyon, CNRS, LaMCoS UMR5259, Université Lyon 1, INSA-Lyon, 69621 Villeurbanne, France;Université de Lyon, CNRS, LaMCoS UMR5259, Université Lyon 1, INSA-Lyon, 69621 Villeurbanne, France;Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, F-69622 Villeurbanne Cedex, France

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2011

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Abstract

This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate. Numerical examples involving smooth and singular data are presented.