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Journal of Scientific Computing

, Volume 52, Issue 1, pp 49–84 | Cite as

Locking-Free Optimal Discontinuous Galerkin Methods for a Naghdi-Type Arch Model

  • Fatih Celiker
  • Li Fan
  • Sheng Zhang
  • Zhimin Zhang
Article

Abstract

In this paper, we introduce and analyze discontinuous Galerkin methods for a Naghdi type arch model. We prove that, when the numerical traces are properly chosen, the methods display optimal convergence uniformly with respect to the thickness of the arch. These methods are thus free from membrane and shear locking. We also prove that, when polynomials of degree k are used, all the numerical traces superconverge with a rate of order h 2k+1. Numerical experiments verifying the above-mentioned theoretical results are displayed.

Keywords

Discontinuous Galerkin methods Naghdi arches Shear and membrane locking Superconvergence 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Fatih Celiker
    • 1
  • Li Fan
    • 1
  • Sheng Zhang
    • 1
  • Zhimin Zhang
    • 1
  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

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