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The Virtual Element Method on Anisotropic Polygonal Discretizations

  • Paola F. Antonietti
  • Stefano Berrone
  • Marco Verani
  • Steffen Weißer
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

In recent years, the numerical treatment of boundary value problems with the help of polygonal and polyhedral discretization techniques has received a lot of attention within several disciplines. Due to the general element shapes an enormous flexibility is gained and can be exploited, for instance, in adaptive mesh refinement strategies. The Virtual Element Method (VEM) is one of the new promising approaches applicable on general meshes. Although polygonal element shapes may be highly adapted, the analysis relies on isotropic elements which must not be very stretched. But, such anisotropic element shapes have a high potential in the discretization of interior and boundary layers. Recent results on anisotropic polygonal meshes are reviewed and the Virtual Element Method is applied on layer adapted meshes containing isotropic and anisotropic polygonal elements.

Notes

Acknowledgements

P.F.A. has been partially funded by SIR starting grant n. RBSI14VT0S funded by the Italian Ministry of Education, Universities and Research (MIUR). P.F.A., S.B. and M.V. thank INdAM-GNCS.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Paola F. Antonietti
    • 1
  • Stefano Berrone
    • 2
  • Marco Verani
    • 1
  • Steffen Weißer
    • 3
  1. 1.MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Dipartimento di Scienze MatematichePolitecnico di TorinoTorinoItaly
  3. 3.Universität des SaarlandesFR MathematikSaarbrückenGermany

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