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

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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.

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Authors and Affiliations

  1. Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    Lin Mu

  2. Division of Mathematical Sciences, National Science Foundation, Arlington, VA, 22230, USA

    Junping Wang

  3. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Xiu Ye

Authors
  1. Lin Mu
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  2. Junping Wang
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  3. Xiu Ye
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Correspondence to Lin Mu.

Additional information

Lin Mu’s research is based upon work supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under award number ERKJE45; and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT-Battelle, LLC, for the U.S. Department of Energy under Contract DE-AC05-00OR22725. Junping Wang was supported by the NSF IR/D program, while working at National Science Foundation. However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. Xiu Ye was supported in part by National Science Foundation Grant DMS-1620016.

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Mu, L., Wang, J. & Ye, X. A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form. J Sci Comput 75, 782–802 (2018). https://doi.org/10.1007/s10915-017-0564-y

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  • DOI: https://doi.org/10.1007/s10915-017-0564-y

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