Multilevel methods are generally based on a splitting of the solution space associated with a nested sequence of coarser grids. Besides the straightforward application of extrapolation on the grid system, we propose to use extrapolation implicitly, similar to multigrid tau-extrapolation. This implicit extrapolation, when applied to linear finite elements is related to the p-version of the finite element method. The method depends on a stability condition which must be enforced by a suitable modification of the problem.

Keywords: Implicit extrapolation, multigrid, multilevel subspace splitting

AMS Classification: 65N22, 65N50, 65N55