Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems

Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, L. Donatella; Russo, Alessandro

doi:10.5802/smai-jcm.40

Beirão da Veiga, Lourenço ¹ ; Brezzi, Franco ² ; Marini, L. Donatella ³ ; Russo, Alessandro ¹

¹ Dipartimento di Matematica e Applicazioni, Università di Milano - Bicocca, Via Cozzi 55, I-20153, Milano, Italy and IMATI-CNR, Via Ferrata 1, I-27100 Pavia, Italy
² IMATI-CNR, Via Ferrata 1, I-27100 Pavia, Italy
³ Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, I-27100 Pavia, Italy and IMATI-CNR, Via Ferrata 1, I-27100 Pavia, Italy

The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 399-416.

Résumé

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 $0 - f o r m s$ , 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.

Publié le : 2018-11-19

MR Zbl

DOI : 10.5802/smai-jcm.40

Classification : 65N30
Mots clés : Virtual Element Methods, Serendipity, Magnetostatic problems, Vector Potential

Affiliations des auteurs :

Beirão da Veiga, Lourenço ¹ ; Brezzi, Franco ² ; Marini, L. Donatella ³ ; Russo, Alessandro ¹

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     title = {Virtual {Element} approximations of the {Vector} {Potential} {Formulation} of {Magnetostatic} problems},
     journal = {The SMAI Journal of computational mathematics},
     pages = {399--416},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, L. Donatella; Russo, Alessandro. Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems. The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 399-416. doi : 10.5802/smai-jcm.40. http://www.numdam.org/articles/10.5802/smai-jcm.40/

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