A note on convergence of V-cycle nonconforming multigrid methods1

摘要

In this paper, the nonconforming multigrid methods are studied, i.e., the fine mesh spaces and coarse mesh spaces also use the same nonconforming finite element. Contrary to the observation by Chen [Convergence of multigrid method for nonconforming method, pre print, 1996], even if quadratic forms are not changed on coarse meshes, V-cycle nonconforming multigrid methods still can converge. The key of our methods is the choice of a “good” intergrid operator. Moreover, optimal convergent order of our V-cycle nonconforming multigrid methods is obtained.