Upscaling Techniques Based on Subspace Corrections and Coarse-grid Approximations
نویسنده
چکیده
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 signii-cantly fewer unknowns, describing the behaviour of the solution of the ne-grid problem in suitable subspaces of the nite-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 up-scaling. We sketch several schemes for recursive approximation of the Schur-complement and report on the results of numerical experiments.
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