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Design and implementation of a multiscale mixed method based on a nonoverlapping domain decomposition procedure

Author

Listed:
  • Francisco, A.
  • Ginting, V.
  • Pereira, F.
  • Rigelo, J.

Abstract

We use a nonoverlapping iterative domain decomposition procedure based on the Robin interface condition to develop a new multiscale mixed method to compute the velocity field in heterogeneous porous media. Hybridized mixed finite elements are used for the spatial discretization of the equations. We define local, multiscale mixed basis functions to represent the discrete solutions in subdomains. Appropriate subspaces of the vector space spanned by these basis functions can be considered in the numerical approximations of heterogeneous porous media flow problems. The balance between numerical accuracy and numerical efficiency is determined by the choice of these subspaces. A detailed description of the numerical method is presented. Following that, numerical experiments are discussed to illustrate the important features of the new procedure and its comparison to the traditional fine grid simulations.

Suggested Citation

  • Francisco, A. & Ginting, V. & Pereira, F. & Rigelo, J., 2014. "Design and implementation of a multiscale mixed method based on a nonoverlapping domain decomposition procedure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 125-138.
    • Handle: RePEc:eee:matcom:v:99:y:2014:i:c:p:125-138
    DOI: 10.1016/j.matcom.2013.04.022
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    References listed on IDEAS

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    1. Pereira, F. & Rahunanthan, A., 2011. "A semi-discrete central scheme for the approximation of two-phase flows in three space dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2296-2306.
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    Cited by:

    1. Ali, Alsadig & Mankad, Het & Pereira, Felipe & Sousa, Fabrício S., 2020. "The multiscale perturbation method for second order elliptic equations," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    2. Rocha, Franciane F. & Mankad, Het & Sousa, Fabricio S. & Pereira, Felipe, 2022. "The multiscale perturbation method for two-phase reservoir flow problems," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    3. Guiraldello, Rafael T. & Ausas, Roberto F. & Sousa, Fabricio S. & Pereira, Felipe & Buscaglia, Gustavo C., 2019. "Interface spaces for the Multiscale Robin Coupled Method in reservoir simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 103-119.

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