Volume 12, Issue 4
Stable Mixed Element Schemes for Plate Models on Multiply-Connected Domains

Shuo Zhang

Adv. Appl. Math. Mech., 12 (2020), pp. 1008-1034.

Published online: 2020-06

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  • Abstract

In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. Constructing a regular decomposition of $H_0(rot,\Omega)$ and a Helmholtz decomposition of its dual, we develop mixed formulations of the models which are equivalent to the primal ones respectively and which are uniformly stable. We then present frameworks of designing uniformly stable mixed finite element schemes and of generating primal finite element schemes from the mixed ones. Specific finite elements are given under the frameworks as an example, and the primal scheme obtained coincides with a Durán-Liberman scheme which was constructed originally on simply-connected domains. Optimal solvers are constructed for the schemes.

  • Keywords

Reissner-Mindlin plate, Kirchhoff plate, multiply-connected domain, uniformly optimal solver, regular decomposition.

  • AMS Subject Headings

65N30, 74K20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-12-1008, author = {Shuo Zhang , }, title = {Stable Mixed Element Schemes for Plate Models on Multiply-Connected Domains}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {4}, pages = {1008--1034}, abstract = {

In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. Constructing a regular decomposition of $H_0(rot,\Omega)$ and a Helmholtz decomposition of its dual, we develop mixed formulations of the models which are equivalent to the primal ones respectively and which are uniformly stable. We then present frameworks of designing uniformly stable mixed finite element schemes and of generating primal finite element schemes from the mixed ones. Specific finite elements are given under the frameworks as an example, and the primal scheme obtained coincides with a Durán-Liberman scheme which was constructed originally on simply-connected domains. Optimal solvers are constructed for the schemes.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0081}, url = {http://global-sci.org/intro/article_detail/aamm/16938.html} }
TY - JOUR T1 - Stable Mixed Element Schemes for Plate Models on Multiply-Connected Domains AU - Shuo Zhang , JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 1008 EP - 1034 PY - 2020 DA - 2020/06 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0081 UR - https://global-sci.org/intro/article_detail/aamm/16938.html KW - Reissner-Mindlin plate, Kirchhoff plate, multiply-connected domain, uniformly optimal solver, regular decomposition. AB -

In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. Constructing a regular decomposition of $H_0(rot,\Omega)$ and a Helmholtz decomposition of its dual, we develop mixed formulations of the models which are equivalent to the primal ones respectively and which are uniformly stable. We then present frameworks of designing uniformly stable mixed finite element schemes and of generating primal finite element schemes from the mixed ones. Specific finite elements are given under the frameworks as an example, and the primal scheme obtained coincides with a Durán-Liberman scheme which was constructed originally on simply-connected domains. Optimal solvers are constructed for the schemes.

Shuo Zhang. (2020). Stable Mixed Element Schemes for Plate Models on Multiply-Connected Domains. Advances in Applied Mathematics and Mechanics. 12 (4). 1008-1034. doi:10.4208/aamm.OA-2019-0081
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