We introduce and analyze a discontinuous Galerkin method for a time-harmonic eddy current problem formulated in terms of the magnetic field. The scheme is obtained by putting together a DG method for the approximation of the vector field variable representing the magnetic field in the conductor and a DG method for the Laplace equation whose solution is a scalar magnetic potential in the insulator. The transmission conditions linking the two problems are taken into account weakly in the global discontinuous Galerkin scheme. We prove that the numerical method is uniformly stable and obtain quasi-optimal error estimates in the DG-energy norm.

A discontinuous Galerkin method for a time-harmonic eddy current problem / Rodríguez, Ana Alonso; Márquez, Antonio; Meddahi, Salim; Valli, Alberto. - In: CALCOLO. - ISSN 0008-0624. - STAMPA. - 2018, 55:3(2018), pp. 25.1-25.23. [10.1007/s10092-018-0267-2]

### A discontinuous Galerkin method for a time-harmonic eddy current problem

#### Abstract

We introduce and analyze a discontinuous Galerkin method for a time-harmonic eddy current problem formulated in terms of the magnetic field. The scheme is obtained by putting together a DG method for the approximation of the vector field variable representing the magnetic field in the conductor and a DG method for the Laplace equation whose solution is a scalar magnetic potential in the insulator. The transmission conditions linking the two problems are taken into account weakly in the global discontinuous Galerkin scheme. We prove that the numerical method is uniformly stable and obtain quasi-optimal error estimates in the DG-energy norm.
##### Scheda breve Scheda completa Scheda completa (DC)
2018
3
Rodríguez, Ana Alonso; Márquez, Antonio; Meddahi, Salim; Valli, Alberto
A discontinuous Galerkin method for a time-harmonic eddy current problem / Rodríguez, Ana Alonso; Márquez, Antonio; Meddahi, Salim; Valli, Alberto. - In: CALCOLO. - ISSN 0008-0624. - STAMPA. - 2018, 55:3(2018), pp. 25.1-25.23. [10.1007/s10092-018-0267-2]
File in questo prodotto:
File
AMV_DGEddy_rev.pdf

Open Access dal 01/10/2019

Descrizione: Articolo
Tipologia: Post-print referato (Refereed author’s manuscript)
Dimensione 357.24 kB

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11572/211701`