Error estimates of upscaled poroelastic models in thin domains for hybrid modeling via heterogeneous domain decomposition

Abstract Knowledge-driven model reduction techniques, such as asymptotic reduction and averaging, are widely employed to simplify the computational complexity of multiphysics systems exhibiting scale separation. In this work, we analyse a vertically averaged biphasic model for thin poroelastic materials and derive error estimates to assess its accuracy and identify key error sources. In particular, we focus on errors arising due to small-scale heterogeneity or transient small-scale dynamics. By analyzing the spatial and temporal behavior of these errors, we develop hybrid computational algorithms based on heterogeneous domain decomposition, where full and reduced models are applied in different subregions of the computational domain. Specifically, we propose: (1) a spatial domain decomposition to address errors from small-scale heterogeneity and (2) a temporal domain decomposition to manage diminishing small-scale transient errors. Numerical experiments on a 2D poro-elastic material validate our analytical error estimates and demonstrate that the proposed hybrid approaches significantly improve both accuracy and computational efficiency.