In this paper we consider new upscaling and homogenization methods for the pressure equation that are less sensitive to the boundary condition assumptions than many other published methods. We start from the discretized pressure equation and rely on the construction of subproblems with significantly fewer unknowns, describing the behaviour of the solution of the finegrid problem in suitable subspaces of the finite-element space. We utilize ideas known from multilevel methods such as operator-dependent interpolation and we clarify the part of Schur-complement approximations in the context of upscaling. We sketch several schemes for recursive approximation of the Schurcomplement and report on the results of numerical experiments
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