We consider the use of nodal and edge Virtual Element spaces for the discretization of magnetostatic problems in two dimensions, following the variational formulation of Kikuchi. In addition, we present a novel Serendipity variant of the same spaces that allow to save many internal degrees of freedom. These Virtual Element Spaces of different type can be useful in applications where an exact sequence is particularly convenient, together with commuting-diagram interpolation operators, as is definitely the case in electromagnetic problems. We prove stability and optimal error estimates, and we check the performance with some academic numerical experiments
Beirao da Veiga, L., Brezzi, F., Dassi, F., Marini, L., Russo, A. (2017). Virtual Element approximation of 2D magnetostatic problems. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 327, 173-195 [10.1016/j.cma.2017.08.013].
Virtual Element approximation of 2D magnetostatic problems
Beirao da Veiga, L.;Dassi, F.;Russo, A.
2017
Abstract
We consider the use of nodal and edge Virtual Element spaces for the discretization of magnetostatic problems in two dimensions, following the variational formulation of Kikuchi. In addition, we present a novel Serendipity variant of the same spaces that allow to save many internal degrees of freedom. These Virtual Element Spaces of different type can be useful in applications where an exact sequence is particularly convenient, together with commuting-diagram interpolation operators, as is definitely the case in electromagnetic problems. We prove stability and optimal error estimates, and we check the performance with some academic numerical experiments
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