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Lourenço Beirão da Veiga; Franco Brezzi; L. Donatella Marini; Alessandro Russo
Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems
SMAI-Journal of computational mathematics, 4 (2018), p. 399-416, doi: 10.5802/smai-jcm.40
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Class. Math.: 65N30
Mots clés: Virtual Element Methods, Serendipity, Magnetostatic problems, Vector Potential

Abstract

We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the classical Vector Potential formulation. The Vector Potential is treated as a triplet of $0\!-\!forms$, approximated by nodal VEM spaces. However this is not done using three classical $H^1$-conforming nodal Virtual Elements, and instead we use the Stokes Elements introduced originally in the paper Divergence free Virtual Elements for the Stokes problem on polygonal meshes (ESAIM Math. Model. Numer. Anal. 51 (2017), 509–535) for the treatment of incompressible fluids.

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