Computational multiscale methods for linear heterogeneous poroelasticity

Robert Altmann Tsz Shun Eric CHUNG Roland Maier Daniel Peterseim Sai-Mang Pun

Numerical Analysis and Scientific Computing mathscidoc:1910.43527

arXiv preprint arXiv:1801.00615, 2018.1
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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@inproceedings{robert2018computational,
  title={Computational multiscale methods for linear heterogeneous poroelasticity},
  author={Robert Altmann, Tsz Shun Eric CHUNG, Roland Maier, Daniel Peterseim, and Sai-Mang Pun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181956558692056},
  booktitle={arXiv preprint arXiv:1801.00615},
  year={2018},
}
Robert Altmann, Tsz Shun Eric CHUNG, Roland Maier, Daniel Peterseim, and Sai-Mang Pun. Computational multiscale methods for linear heterogeneous poroelasticity. 2018. In arXiv preprint arXiv:1801.00615. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020181956558692056.
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