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(2001) Key: citeulike:11271590
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Geometric multigrid can be used directly for Stokes by (a) using interpolation operators that make sense for pressure and velocity independently and (b) using smoothers that respect the indefinite nature of the problem. Trottenberg's book has lots of details, but an example of a good smoother is due to Vanka. It is a multiplicative overlapping Schwarz method that uses domains obtained by taking a pressure node, adding all velocity dofs that touch it, then assembling that block problem (or extracting it from the matrix), solving, updating the state vector for all dofs under the block solve, then moving to the next pressure node. Efficiently implementing these with assembled matrices or continuous finite elements is unfortunately, somewhat problematic. DG is very nice for this purpose.
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