Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective

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Abstract

We study discontinuous Galerkin approximations of the p-biharmonic equation for p ∈ (1, ∞) from a variational perspective. We propose a discrete variational formulation of the problem based on an appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a semicontinuity argument. We also present numerical experiments aimed at testing the robustness of the method.

Original languageEnglish
Pages (from-to)328-349
Number of pages22
JournalElectronic Transactions on Numerical Analysis
Volume41
Publication statusPublished - 2014

Keywords

  • Discontinuous Galerkin finite element method
  • Discrete variational problem
  • p-biharmonic equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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