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COMPUTATIONAL MULTISCALE METHODS FOR LINEAR HETEROGENEOUS POROELASTICITY

Robert Altmann1, Eric Chung2, Roland Maier3, Daniel Peterseim3, Sai-Mang Pun4   

  • Received:2018-09-07 Revised:2018-12-16 Online:2020-01-15 Published:2020-01-15
  • Supported by:

    The authors acknowledge support from the Germany/Hong Kong Joint Research Scheme sponsored by the German Academic Exchange Service (DAAD) under the project 57334719 and the Research Grants Council of Hong Kong with reference number GCUHK405/16. Further, the authors thank the Hausdorff Institute for Mathematics in Bonn for the kind hospitality during the trimester program on multiscale problems in 2017. Daniel Peterseim also acknowledges support by the Sino-German Science Center on the occasion of the Chinese-German Workshop on Computational and Applied Mathematics in Shanghai 2017.

Robert Altmann, Eric Chung, Roland Maier, Daniel Peterseim, Sai-Mang Pun. COMPUTATIONAL MULTISCALE METHODS FOR LINEAR HETEROGENEOUS POROELASTICITY[J]. Journal of Computational Mathematics, 2020, 38(1): 41-57.

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough numerical treatment. In this paper, we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity. Therein, local corrector problems are constructed in line with the static equations, whereas we propose to consider the full system. This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure. We prove the optimal first-order convergence of this method and verify the result by numerical experiments.

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