Error Analysis of an Equation Error Method for the Identification of the Diffusion Coefficient in a Quasi-linear Parabolic Differential Equation

@article{Hanke1998ErrorAO,
  title={Error Analysis of an Equation Error Method for the Identification of the Diffusion Coefficient in a Quasi-linear Parabolic Differential Equation},
  author={Martin Hanke and Otmar Scherzer},
  journal={SIAM Journal of Applied Mathematics},
  year={1998},
  volume={59},
  pages={1012-1027}
}
We consider the inverse problem of reconstructing the diiusion coeecient in a quasilinear parabolic diierential equation in divergence form from measurements of the solution at a nite number of points in the interior of the domain. An equation error method is developed which transforms the inverse problem into a system of linear operator equations for the diiusion coeecient, and which can be solved by the conjugate gradient method in a very eecient and stable manner. A detailed error analysis… CONTINUE READING
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