An enhanced multiscale model for porous media flows by means of an adaptive local trace mode analysis
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The underlying context is the Multiscale Hybrid Mixed method, which is a strategy for efficient simulations of Darcy’s problems with strongly varying solutions. The method is based on a partition of the porous media by polytopal macro subregions, where divergence-conforming finite element pairs for flux and pressure approximations are considered. The flux components interacting with the subregion boundaries have normal components strongly constrained by a finite element trace space, whilst internal flux components and pressure spaces are fixed, with sufficient resolution to solve local field details. Starting from a coarser resolution level, we propose and evaluate an a priori adaptive selective enrichment of the trace approximation by means of a mode analysis of Steklov type.
