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Journal of Scientific Computing

, Volume 75, Issue 2, pp 782–802 | Cite as

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

  • Lin Mu
  • Junping Wang
  • Xiu Ye
Article
  • 186 Downloads

Abstract

A new finite element method is developed 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. 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.

Keywords

Weak Galerkin Finite element methods Weak gradient The Reissner–Mindlin plate Polygonal partitions 

Mathematics Subject Classification

Primary 65N15 65N30 Secondary 35J50 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Computer Science and Mathematics DivisionOak Ridge National LaboratoryOak RidgeUSA
  2. 2.Division of Mathematical SciencesNational Science FoundationArlingtonUSA
  3. 3.Department of MathematicsUniversity of Arkansas at Little RockLittle RockUSA

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