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 -
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.