The objective of this workshop was to bring together researchers working in multiscale simulations with emphasis on multigrid methods and multiscale ﬁnite element methods, aiming at chieving of better understanding and synergy between these methods. The goal of multiscale ﬁnite element methods, as upscaling methods, is to compute coarse scale solutions of the underlying equations as accurately as possible. On the other hand, multigrid methods attempt to solve ﬁne-scale equations rapidly using a hierarchy of coarse spaces. Multigrid methods need “good” coarse scale spaces for their eﬃciency. The discussions of this workshop partly focused on approximation properties of coarse scale spaces and multigrid convergence. Some other presentations were on upscaling, domain decomposition methods and nonlinear multiscale methods. Some researchers discussed applications of these methods to reservoir simulations, as well as to simulations of ﬁltration, insulating materials, and turbulence.
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Achi Brandt, Oleg Iliev, Yalchin Efendiev, Mini-Workshop: Numerical Upscaling for Flow Problems: Theory and Applications. Oberwolfach Rep. 6 (2009), no. 1, pp. 681–724DOI 10.4171/OWR/2009/12