TY - JOUR
T1 - A $T-ψ$ Finite Element Method for a Nonlinear Degenerate Eddy Current Model  with Ferromagnetic Materials
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 636
EP - 663
PY - 2015
DA - 2015/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/505.html
KW - nonlinear degenerate eddy current problem, $T-\psi$ method, nodal elements, convergence, and error estimates.
AB - <p style="text-align: justify;">This paper is devoted to the study of a fully discrete $T-\psi$ 8finite element method
based on $H$-decomposition to solve a nonlinear degenerate transient eddy current problem with
ferromagnetic materials. Here, the ferromagnetic properties are linked by a power material law.
We first design a nonlinear time-discrete scheme for approximation in suitable function spaces. We
show the well-posedness of the semidiscrete problem and prove the convergence of the nonlinear
scheme by the Minty-Browder technique. Finally, we suggest a fully discrete scheme, derive its
error estimate and give some numerical experiments to validate the theoretical result.</p>