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A V-cycle multigrid method for the Hellan-Herrmann-Johnson (HHJ)discretization of the Kirchhoff plate bending problems is developed in thispaper. It is shown that the contraction number of the V-cycle multigrid HHJmixed method is bounded away from one uniformly with respect to the mesh size.The uniform convergence is achieved for the V-cycle multigrid method with onlyone smoothing step and without full elliptic regularity. The key is a stabledecomposition of the kernel space which is derived from an exact sequence ofthe HHJ mixed method, and the strengthened Cauchy Schwarz inequality. Somenumerical experiments are provided to confirm the proposed V-cycle multigridmethod. The exact sequences of the HHJ mixed method and the correspondingcommutative diagram is of some interest independent of the current context.

Multigrid Methods for Hellan-Herrmann-Johnson Mixed Method of Kirchhoff Plate Bending Problems