On the Tree Gauge in Magnetostatics

Francesca Rapetti, Ana Alonso Rodríguez and Eduardo De Los Santos
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Francesca Rapetti: Laboratoire Mathématiques & Interactions, Université Côte d’Azur, Parc Valrose, F-06108 Nice, France
Ana Alonso Rodríguez: Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, Povo, I-38123 Trento, Italy
Eduardo De Los Santos: Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, Povo, I-38123 Trento, Italy

J, 2022, vol. 5, issue 1, 1-12

Abstract: We recall the classical tree-cotree technique in magnetostatics. (1) We extend it in the frame of high-order finite elements in general domains. (2) We focus on its connection with the question of the invertibility of the final algebraic system arising from a high-order edge finite element discretization of the magnetostatic problem formulated in terms of the magnetic vector potential. With the same purpose of invertibility, we analyse another classically used condition, the Coulomb gauge. (3) We conclude by underlying that the two gauges can be naturally considered in a high order framework without any restriction on the topology of the domain.

Keywords: magnetic vector potential; high order edge finite elements; tree gauge; Coulomb gauge (search for similar items in EconPapers)
JEL-codes: I1 I10 I12 I13 I14 I18 I19 (search for similar items in EconPapers)
Date: 2022
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