Energy conserving Galerkin finite element methods for the Maxwell-Klein-Gordon system

• Verfasst von: Ma, Chupeng [VerfasserIn]
• Verfasst von: Cao, Liqun [VerfasserIn]
• Verfasst von: Lin, Yanping [VerfasserIn]
• Titel: Energy conserving Galerkin finite element methods for the Maxwell-Klein-Gordon system
• Verf.angabe: Chupeng Ma, Liqun Cao, and Yanping Lin
• E-Jahr: 2020
• Jahr: 29 April 2020
• Umfang: 28 S.
• Fussnoten: Gesehen am 12.08.2020
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on numerical analysis
• Ort Quelle: Philadelphia, Pa. : SIAM, 1966
• Jahr Quelle: 2020
• Band/Heft Quelle: 58(2020), 2, Seite 1339-1366
• ISSN Quelle: 1095-7170
• DOI: doi:10.1137/17M1158690
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 2nd-order scheme
• Sach-SW: backward error analysis
• Sach-SW: convergence
• Sach-SW: energy conservation
• Sach-SW: equation
• Sach-SW: error estimates
• Sach-SW: finite element method
• Sach-SW: Maxwell-Klein-Gordon
• Sach-SW: time integration scheme
• K10plus-PPN: 1726865843

Abstract

In this paper, we consider the Galerkin finite element methods for the Maxwell- Klein-Gordon system in the Coulomb gauge. We propose a semidiscrete finite element method for the system with the mixed finite element approximation of the vector potential. Energy conservation and error estimates are established for this scheme. A novel energy conserving time integration scheme is presented for solving the semidiscrete system. The existence and uniqueness of solutions to the fully discrete system are proved under some assumptions. Numerical experiments are carried out to support our theoretical analysis.