TY - JOUR
T1 - Computational Multiscale Methods for Linear Heterogeneous Poroelasticity
AU - Altmann , Robert
AU - Chung , Eric T.
AU - Maier , Roland
AU - Peterseim , Daniel
AU - Pun , Sai-Mang
JO - Journal of Computational Mathematics
VL - 1
SP - 41
EP - 57
PY - 2020
DA - 2020/02
SN - 38
DO - http://doi.org/10.4208/jcm.1902-m2018-0186
UR - https://global-sci.org/intro/article_detail/jcm/13684.html
KW - Poroelasticity, Heterogeneous media, Numerical homogenization, Multiscale methods.
AB - <p style="text-align: justify;"><span style="font-size: 20px;">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 benefiting 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.</span></p>