Two variants of magnetic diffusivity stabilized finite element methods for the magnetic induction equation. (24th May 2019)

• Record Type: Journal Article
• Authors: Wacker, Benjamin
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 13(2019)
• Page Start: 4554
• Page End: 4569
• Publication Date: 2019-05-24
• Subjects: layer phenomena -- local projection stabilization -- magnetic diffusivity -- magnetic induction equation -- stabilized finite element methods -- stability and convergence analysis; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5680
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We consider the time‐dependent magnetic induction model where the sought magnetic field interacts with a prescribed velocity field. This coupling results in an additional force term and time dependence in Maxwell's equation. We propose two different magnetic diffusivity stabilized continuous nodal‐based finite element methods for this problem. The first formulation simply adds artificial magnetic diffusivity to the partial differential equation, whereas the second one uses a local projected magnetic diffusivity as stabilization. We describe those methods and analyze them semi‐discretized in space to get bounds on stabilization parameters where we distinguish equal‐order elements and Taylor‐Hood elements. Different numerical experiments are performed to illustrate our theoretical findings.