We consider, as a simple model problem, the application of virtual element methods (VEMs) to the linear magnetostatic three-dimensional problem in the formulation of 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 H1-conforming (0-forms), H(curl)-conforming (1-forms), and H(div)-conforming (2-forms) functional spaces in three dimensions, and they could surely be useful for other problems and in more general contexts.

Beirão Da Veiga, L., Brezzi, F., Dassi, F., Marini, L., Russo, A. (2018). A family of three-dimensional virtual elements with applications to magnetostatics. SIAM JOURNAL ON NUMERICAL ANALYSIS, 56(5), 2940-2962 [10.1137/18M1169886].

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

Beirão Da Veiga, L;Dassi, F;Russo, A
2018

Abstract

We consider, as a simple model problem, the application of virtual element methods (VEMs) to the linear magnetostatic three-dimensional problem in the formulation of 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 H1-conforming (0-forms), H(curl)-conforming (1-forms), and H(div)-conforming (2-forms) functional spaces in three dimensions, and they could surely be useful for other problems and in more general contexts.
Articolo in rivista - Articolo scientifico
Magnetostatic problems; Serendipity; Virtual element methods;
Magnetostatic problems; Serendipity; Virtual element methods; Numerical Analysis; Computational Mathematics; Applied Mathematics
English
2018
56
5
2940
2962
reserved
Beirão Da Veiga, L., Brezzi, F., Dassi, F., Marini, L., Russo, A. (2018). A family of three-dimensional virtual elements with applications to magnetostatics. SIAM JOURNAL ON NUMERICAL ANALYSIS, 56(5), 2940-2962 [10.1137/18M1169886].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/212791
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