Treatments of discontinuity and bubble functions in the multigrid method

Abstract

When multilevel finite element spaces are not nested, different intergrid transfer operators would lead to different multigrid algorithms. It is proposed in this paper that discontinuous functions be averaged to continuous functions and that the bubble functions be discarded in the multigrid transferring. Applications of the techniques to various problems are presented with convergence analysis. Numerical comparisons with other existing methods are provided.