We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field H on each edge, and the vertex values of the Lagrange multiplier p (used to enforce the solenoidality of the magnetic induction B=μH). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called “first kind Nédélec” elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions

Beirão da Veiga, L., Brezzi, F., Dassi, F., Marini, L., Russo, A. (2018). Lowest order Virtual Element approximation of magnetostatic problems. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 332, 343-362 [10.1016/j.cma.2017.12.028].

### Lowest order Virtual Element approximation of magnetostatic problems

#### Abstract

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field H on each edge, and the vertex values of the Lagrange multiplier p (used to enforce the solenoidality of the magnetic induction B=μH). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called “first kind Nédélec” elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions
##### Scheda breve Scheda completa Scheda completa (DC)
Articolo in rivista - Articolo scientifico
Finite Element Methods, Virtual Element Methods, Magnetostatic problems, Serendipity.
English
2018
332
343
362
open
Beirão da Veiga, L., Brezzi, F., Dassi, F., Marini, L., Russo, A. (2018). Lowest order Virtual Element approximation of magnetostatic problems. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 332, 343-362 [10.1016/j.cma.2017.12.028].
File in questo prodotto:
File
1-s2.0-S004578251830001X-main.pdf

accesso aperto

Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Dimensione 1.91 MB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/180493`