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.
VEM approximations of the Vector Potential Formulation of Magnetostatic problems
L. D. Marini;
2018-01-01
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.File in questo prodotto:
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