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Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method

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Abstract

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments are presented and discussed.

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Authors and Affiliations

  1. Department of Economics and Business Administration, University of Agder, Servicebox 422, 4604, Kristiansand, Norway

    T. K. Nilssen

  2. Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway

    K. H. Karlsen

  3. Centre for Integrated Petroleum Research, P. O. Box 7800, 5020, Bergen, Norway

    T. Mannseth

  4. Department of Mathematics, University of Bergen, Johannes Brunsgt. 12, 5008, Bergen, Norway

    T. Mannseth & X.-C. Tai

Authors
  1. T. K. Nilssen
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  2. K. H. Karlsen
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  3. T. Mannseth
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  4. X.-C. Tai
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Corresponding author

Correspondence to T. K. Nilssen.

Additional information

This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431.

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Nilssen, T.K., Karlsen, K.H., Mannseth, T. et al. Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method. Comput Geosci 13, 317–329 (2009). https://doi.org/10.1007/s10596-008-9120-z

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  • DOI: https://doi.org/10.1007/s10596-008-9120-z

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