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The fully nonconforming virtual element method for biharmonic problems

Mathematical Models and Methods in Applied Sciences, ISSN: 0218-2025, Vol: 28, Issue: 2, Page: 387-407
2018
  • 115
    Citations
  • 0
    Usage
  • 14
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    115
    • Citation Indexes
      115
  • Captures
    14

Article Description

In this paper, we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numerical results to assess the validity of the theoretical estimates.

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