A FAMILY OF THREE-DIMENSIONAL VIRTUAL ELEMENTS WITH APPLICATIONS TO MAGNETOSTATICS

We consider, as a simple model problem, the application of virtual element methods (VEMs) to the linear magnetostatic three-dimensional problem in the formulation of Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a gen...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on numerical analysis 2018-01, Vol.56 (5), p.2940-2962
Main Authors: DAVEIGA, L. BEIRÃO, BREZZI, F., DASSI, F., MARINI, L. D., RUSSO, A.
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider, as a simple model problem, the application of virtual element methods (VEMs) to the linear magnetostatic three-dimensional problem in the formulation of Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of H¹-conforming (0-forms), H(curl)-conforming (1-forms), and H(div)-conforming (2-forms) functional spaces in three dimensions, and they could surely be useful for other problems and in more general contexts.
ISSN:0036-1429
1095-7170
DOI:10.1137/18M1169886