A new analysis of discontinuous Galerkin methods for a fourth order variational inequality

Jintao Cui, Yi Zhang

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1 Citation (Scopus)

Abstract

We study a family of discontinuous Galerkin methods for the displacement obstacle problem of Kirchhoff plates on two and three dimensional convex polyhedral domains, which are characterized as fourth order elliptic variational inequalities of the first kind. We prove that the error in an H 2 -like energy norm is O(h α ) for the quadratic method, where α∈([Formula presented],1] is determined by the geometry of the domain. Under additional assumptions on the contact set such that the solution has improved regularity, we derive the optimal error estimate with α∈(1,[Formula presented]) for the cubic method. Numerical experiments demonstrate the performance of the methods and confirm the theoretical results.

Original languageEnglish
Pages (from-to)531-547
Number of pages17
JournalComputer Methods in Applied Mechanics and Engineering
Volume351
DOIs
Publication statusPublished - 1 Jul 2019

Keywords

  • Discontinuous Galerkin methods
  • Displacement obstacle
  • Error estimate
  • Fourth order variational inequality

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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