The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids
For the numerical solution of elliptic boundary value problems discretized by finite element schemes on unstructured grids the author develops an abstract framework of the auxiliary space method. This is an optimal preconditioning technique that results from the proper combination of an appropriate smoother and a structured auxiliary grid and can be interpreted as a two-level nonnested multigrid preconditioner. Examples include the use of a -- nested coarse grid space as an auxiliary space, -- lower-order element as an auxiliary space for a higher-order element, -- conforming element as an auxiliary space for a nonconforming element.
scientific article; zbMATH DE number 878404
scientific article