Nonconforming finite elements and the Cascade iteration

Abstract

We derive sucient conditions under which the Cascade iteration applied to nonconforming nite element discretizations yields an optimal solver. Key ingredients are optimal error estimates of such discretizations, which we therefore study in detail. We derive a new, ecient modied Morley nite element method. Optimal Cascade iterations are obtained for problems of second, and using a new smoother, of fourth order as well as for the Stokes problem.