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• W2064699269 abstract "Multigrid algorithms for $C^0$ interior penalty methods for fourth order elliptic boundary value problems on polygonal domains are studied in this paper. It is shown that V-cycle, F-cycle and W-cycle algorithms are contractions if the number of smoothing steps is sufficiently large. The contraction numbers of these algorithms are bounded by $Cm^{-alpha}$, where m is the number of presmoothing (and postsmoothing) steps, $alpha$ is the index of elliptic regularity, and the positive constant C is mesh-independent. These estimates are established for a smoothing scheme that uses a Poisson solve as a preconditioner, which can be easily implemented because the $C^0$ finite element spaces are standard spaces for second order problems. Furthermore the variable V-cycle algorithm is also shown to be an optimal preconditioner." @default.
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• W2064699269 date "2006-01-01" @default.
• W2064699269 modified "2023-10-15" @default.
• W2064699269 title "Multigrid Algorithms for C0 Interior Penalty Methods" @default.
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• W2064699269 doi "https://doi.org/10.1137/040611835" @default.
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