Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model

Victor M. Calo, Nathan Collier, Antti H. Niemi

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) with a thickness-dependent constant in a norm encompassing the L2-norms of the bending moment, the shear force, the transverse deflection and the rotation vector. We then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p. We show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p+3. We prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non-affine mesh sequences. © 2013 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)2570-2586
Number of pages17
JournalComputers & Mathematics with Applications
Volume66
Issue number12
DOIs
StatePublished - Jan 2014

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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