We consider a strongly heterogeneous medium saturated by an incompressibleviscous fluid as it appears in geomechanical modeling. This poroelasticityproblem suffers from rapidly oscillating material parameters, which calls for athorough numerical treatment. In this paper, we propose a method based on thelocal orthogonal decomposition technique and motivated by a similar approachused for linear thermoelasticity. Therein, local corrector problems areconstructed in line with the static equations, whereas we propose to considerthe full system. This allows to benefit from the given saddle point structureand results in two decoupled corrector problems for the displacement and thepressure. We prove the optimal first-order convergence of this method andverify the result by numerical experiments.
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