Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {S.~Knapek},
  title = {Upscaling techniques based on subspace correction and
		  coarse-grid approximation},
  journal = {InSitu},
  year = {1998},
  optkey = {},
  volume = {22},
  number = {1},
  pages = {35--58},
  optmonth = {},
  note = {Special issue on reservoir simulation},
  annote = {article,256C},
  abstract = {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.},
  ps = { 1}