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arXiv · 1804.10497

A family of three-dimensional virtual elements with applications to magnetostatic

L. Beirão da Veiga·F. Brezzi·F. Dassi·L. D. Marini·A. Russo
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Abstract

We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H({\rm {\bf curl}})$-conforming ($1$-forms), and $H({\rm div})$-conforming ($2$-forms) functional spaces in three dimensions, and they would surely be useful for other problems and in more general contexts.

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L. Beirão da Veiga, F. Brezzi, F. Dassi, L. D. Marini, A. Russo. 2018-04-27. A family of three-dimensional virtual elements with applications to magnetostatic. https://arxiv.org/abs/1804.10497

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