The hellan-herrmann-johnson method with curved elements

Douglas N. Arnold, Shawn W. Walker

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We study the finite element approximation of the Kirchhoff plate equation on domains with curved boundaries using the Hellan-Herrmann-Johnson (HHJ) method. We prove optimal convergence on domains with piecewise Ck+1 boundary for k ≥ 1 when using a parametric (curved) HHJ space. Computational results are given that demonstrate optimal convergence and how convergence degrades when curved triangles of insufficient polynomial degree are used. Moreover, we show that the lowest order HHJ method on a polygonal approximation of the disk does not succumb to the classic Babuška paradox, highlighting the geometrically nonconforming aspect of the HHJ method.

Original languageEnglish (US)
Pages (from-to)2829-2855
Number of pages27
JournalSIAM Journal on Numerical Analysis
Volume58
Issue number5
DOIs
StatePublished - Oct 14 2020

Bibliographical note

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics

Keywords

  • Babuška paradox
  • Geometric consistency error
  • Kirchhoff plate
  • Mesh-dependent norms
  • Parametric finite elements
  • Simply supported

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