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 H1-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.
Beirão da Veiga, L., Brezzi, F., Marini, L., Russo, A. (2018). Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems. THE SMAI JOURNAL OF COMPUTATIONAL MATHEMATICS, 4, 399-416 [10.5802/smai-jcm.40].
Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems
Beirão da Veiga, L;Russo, A
2018
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 H1-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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