Premium
Two variants of magnetic diffusivity stabilized finite element methods for the magnetic induction equation
Author(s) -
Wacker Benjamin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5680
Subject(s) - thermal diffusivity , magnetic diffusivity , discretization , magnetic field , mathematics , mathematical analysis , finite element method , electromagnetic induction , partial differential equation , coupling (piping) , differential equation , physics , magnetohydrodynamics , thermodynamics , electromagnetic coil , materials science , quantum mechanics , metallurgy
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.