Summary
In the present paper we give a convergence theory for multi-grid methods with transforming smoothers as introduced in [31] applied to a general system of partial differential equations. The theory follows Hackbusch's approach for scalar pde and allows a convergence proof for some well-known multi-grid methods for Stokes- and Navier-Stokes equations as DGS by Brandt-Dinar, [5], TILU from [31] and the SIMPLE-methods by Patankar-Spalding, [23].
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This work was supported in part by Deutsche Forschungsgemeinschaft
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Wittum, G. On the convergence of multi-grid methods with transforming smoothers. Numer. Math. 57, 15–38 (1990). https://doi.org/10.1007/BF01386394
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DOI: https://doi.org/10.1007/BF01386394