Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
[1] S. Knapek. Upscaling techniques based on subspace correction and coarse-grid approximation. InSitu, 22(1):35-58, 1998. Special issue on reservoir simulation.
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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 fine-grid 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 Schur-complement and report on the results of numerical experiments.