2018/04/27 by L. Beirão da Veiga, da Veiga, L. Beirão, Franco Brezzi +7 · 5 citations
Engineering · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1804.10497
openalex publication_date 2018/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 H1-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.