The fully adaptive multigrid method (FAMe) is a finite element based elliptic solver integrating self-adaptivity, error estimation and efficient iterative solution. Refined elements are not restricted to predetermined regions and need not be grouped in patches. Instead, whether an element is refined, is decided individually for each element using an integrated error indicator. The refinement process induces a multilevel structure and therefore a natural decomposition of the solution space into a nested sequence. This can be exploited to define an efficient solver and error estimator.

AMS Classifications: 65N55, 65N15, 65N50

Keywords: fully adaptive multigrid, mesh refinement, virtual global grids, error estimates, multilevel additive Schwarz method