A gradient recovery method based on an oblique projection for the virtual element method

Authors

  • Balaje Kalyanaraman The University of Newcastle, Australia http://orcid.org/0000-0001-6181-1876
  • Bishnu Lamichhane The University of Newcastle, Australia
  • Michael Meylan The University of Newcastle, Australia

DOI:

https://doi.org/10.21914/anziamj.v60i0.14041

Keywords:

Gradient Recovery, Virtual Element Method, Oblique Projection

Abstract

The virtual element method is an extension of the finite element method on polygonal meshes. The virtual element basis functions are generally unknown inside an element and suitable projections of the basis functions onto polynomial spaces are used to construct the elemental stiffness and mass matrices. We present a gradient recovery method based on an oblique projection, where the gradient of the L2-polynomial projection of a solution is projected onto a virtual element space. This results in a computationally efficient numerical method. We present numerical results computing the gradients on different polygonal meshes to demonstrate the flexibility of the method. References
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Author Biographies

Balaje Kalyanaraman, The University of Newcastle, Australia

PhD Candidate School of Mathematical and Physical Sciences

Bishnu Lamichhane, The University of Newcastle, Australia

Senior Lecturer School of Mathematical and Physical Sciences

Michael Meylan, The University of Newcastle, Australia

Associate Professor School of Mathematical and Physical Sciences

Published

2019-10-11

Issue

Section

Proceedings Computational Techniques and Applications Conference