article

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

Authors:

Xuehai HuangAuthors Info & Claims

Journal of Scientific Computing, Volume 76, Issue 2

Pages 673 - 696

https://doi.org/10.1007/s10915-017-0636-z

Published: 01 August 2018 Publication History

Abstract

A V-cycle multigrid method for the Hellan---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 assumption. 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.

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Cited By

Farrell PHamdan AMacLachlan S(2022)A new mixed finite-element method for H 2 elliptic problemsComputers & Mathematics with Applications10.1016/j.camwa.2022.10.024128:C(300-319)Online publication date: 15-Dec-2022
https://dl.acm.org/doi/10.1016/j.camwa.2022.10.024
Sun PHuang X(2018)Quasi-optimal convergence rate for an adaptive hybridizable $$C^0$$C0 discontinuous Galerkin method for Kirchhoff platesNumerische Mathematik10.1007/s00211-018-0953-7139:4(795-829)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s00211-018-0953-7

Multigrid Methods for Hellan---Herrmann---Johnson Mixed Method of Kirchhoff Plate Bending Problems
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
    2. Numerical analysis
2. Theory of computation

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Published In

cover image Journal of Scientific Computing

Journal of Scientific Computing Volume 76, Issue 2

August 2018

653 pages

ISSN:0885-7474

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Copyright © Copyright © 2018 Springer Science+Business Media, LLC, part of Springer Nature.

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Plenum Press

United States

Publication History

Published: 01 August 2018

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Cited By

Farrell PHamdan AMacLachlan S(2022)A new mixed finite-element method for H 2 elliptic problemsComputers & Mathematics with Applications10.1016/j.camwa.2022.10.024128:C(300-319)Online publication date: 15-Dec-2022
https://dl.acm.org/doi/10.1016/j.camwa.2022.10.024
Sun PHuang X(2018)Quasi-optimal convergence rate for an adaptive hybridizable $$C^0$$C0 discontinuous Galerkin method for Kirchhoff platesNumerische Mathematik10.1007/s00211-018-0953-7139:4(795-829)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s00211-018-0953-7

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