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

Authors:
Fatih Celiker;Li Fan;Sheng Zhang;Zhimin Zhang
Affiliations:
Department of Mathematics, Wayne State University, Detroit, USA 48202;Department of Mathematics, Wayne State University, Detroit, USA 48202;Department of Mathematics, Wayne State University, Detroit, USA 48202;Department of Mathematics, Wayne State University, Detroit, USA 48202
Venue:
Journal of Scientific Computing
Year:
2012

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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.