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Title: A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

Abstract

We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of the method with respect to the plate thickness.

Authors:
ORCiD logo [1];  [2];  [3]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  2. National Science Foundation, Arlington, VA (United States). Division of Mathematical Sciences
  3. Univ. of Arkansas, Little Rock, AR (United States). Dept. of Mathematics
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1407722
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Scientific Computing
Additional Journal Information:
Journal Volume: 75; Journal Issue: 2; Journal ID: ISSN 0885-7474
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; weak galerkin; finite element methods; weak gradient; the Reissner-Mindlin plate Polygonal partitions

Citation Formats

Mu, Lin, Wang, Junping, and Ye, Xiu. A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form. United States: N. p., 2017. Web. doi:10.1007/s10915-017-0564-y.
Mu, Lin, Wang, Junping, & Ye, Xiu. A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form. United States. doi:10.1007/s10915-017-0564-y.
Mu, Lin, Wang, Junping, and Ye, Xiu. Wed . "A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form". United States. doi:10.1007/s10915-017-0564-y. https://www.osti.gov/servlets/purl/1407722.
@article{osti_1407722,
title = {A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form},
author = {Mu, Lin and Wang, Junping and Ye, Xiu},
abstractNote = {We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of the method with respect to the plate thickness.},
doi = {10.1007/s10915-017-0564-y},
journal = {Journal of Scientific Computing},
number = 2,
volume = 75,
place = {United States},
year = {2017},
month = {10}
}

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