Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems
The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 399-416.

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.

Published online:
DOI: https://doi.org/10.5802/smai-jcm.40
Classification: 65N30
Keywords: Virtual Element Methods, Serendipity, Magnetostatic problems, Vector Potential
@article{SMAI-JCM_2018__4__399_0,
     author = {Louren\c{c}o Beir\~ao da Veiga and Franco Brezzi and L. Donatella Marini and Alessandro Russo},
     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},
     volume = {4},
     year = {2018},
     doi = {10.5802/smai-jcm.40},
     mrnumber = {3883675},
     zbl = {1416.78024},
     language = {en},
     url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.40/}
}
Lourenço Beirão da Veiga; Franco Brezzi; L. Donatella Marini; Alessandro Russo. Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems. The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 399-416. doi : 10.5802/smai-jcm.40. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.40/

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