Treatments of Discontinuity and Bubble Functions in the Multigrid Method

. 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. AMS (MOS) subject classifications. 65N55, 65N30, 65F10 1. Introduction The multigrid method provides optimal-order algorithms for solving large linear systems of finite element and finite difference equations (cf. [3]). The multigrid theory is well established (cf. [12, 16, 3, 15 and 5]). However, in many situations, the multi-level discrete spaces are nonnested due to the nature of the underlying finite elements ([4, 7--8, 18, 25]) or due to the special structures of grids (cf. [6, 920, 26, 27]). Some special treatments are t..