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Virtual Element and Discontinuous Galerkin Methods

  • F. Brezzi
  • L. D. Marini
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 157)

Abstract

Virtual element methods (VEM) are the latest evolution of the Mimetic Finite Difference Method and can be considered to be more close to the Finite Element approach. They combine the ductility of mimetic finite differences for dealing with rather weird element geometries with the simplicity of implementation of Finite Elements. Moreover, they make it possible to construct quite easily high-order and high-regularity approximations (and in this respect they represent a significant improvement with respect to both FE and MFD methods). In the present paper we show that, on the other hand, they can also be used to construct DG-type approximations, although numerical tests should be done to compare the behavior of DG-VEM versus DG-FEM.

Keywords

Discontinuous Galerkin Virtual elements Mimetic finite differences 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.IUSS-PaviaPaviaItaly
  2. 2.King Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Università di PaviaPaviaItaly

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