Published

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

Long Chen, Jun Hu, and Xuehai Huang

Journal of Scientific Computing (2018) 76: 673.

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ABSTRACT:

A V-cyclemultigridmethodfortheHellan–Herrmann–Johnson(HHJ)
discretization of the Kirchhoff plate bending problems is developed in
this paper. It is shown that the contraction number of the V-cycle
multigrid HHJ mixed 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 only one smoothing step and without full
elliptic regularity assump- tion. The key is a stable decomposition of
the kernel space which is derived from an exact sequence of the HHJ
mixed method, and the strengthened Cauchy Schwarz inequality. Some
numerical experiments are provided to confirm the proposed V-cycle
multigrid method. The exact sequences of the HHJ mixed method and the
corresponding commutative diagram is of some interest independent of
the current context.