About the gauge conditions arising in Finite Element magnetostatic problems. (15th March 2019)

• Record Type: Journal Article
• Authors: Creusé, Emmanuel; Dular, Patrick; Nicaise, Serge
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 6(2019)
• Page Start: 1563
• Page End: 1582
• Publication Date: 2019-03-15
• Subjects: Maxwell equations -- Potential formulations -- Gauge conditions -- Finite element method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.06.030
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we deal with some magnetostatic models considered in vector potential formulations and solved by a Finite Element solver. In order to ensure the uniqueness of the solution, a gauge condition has to be imposed, and several possibilities occur. Moreover, the source term has to be correctly defined to ensure a physically admissible solution. We show the equivalence between some of these choices for several kinds of boundary conditions. Moreover, we highlight their characteristic behaviors on some numerical benchmarks to illustrate our theoretical results.