Abstract
For elliptic partial differential equations with periodically oscillating coefficients which may have large jumps, we prove robust convergence of a two-grid algorithm using a prolongation motivated by the theory of homogenization. The corresponding Galerkin operator on the coarse grid turns out to be a discretization of a diffusion operator with homogenized coefficients obtained by solving discrete cell problems. This two-grid method is then embedded inside a multi-grid cycle extending over both the fine and the coarse scale.
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Received August 10, 1999; revised July 28, 2000
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Neuss, N., Jäger, W. & Wittum, G. Homogenization and Multigrid. Computing 66, 1–26 (2001). https://doi.org/10.1007/s006070170036
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DOI: https://doi.org/10.1007/s006070170036