A $T-ψ$ Finite Element Method for a Nonlinear Degenerate Eddy Current Model with Ferromagnetic Materials
Year: 2015
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 4 : pp. 636–663
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2015-IJNAM-505
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 4 : pp. 636–663
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: nonlinear degenerate eddy current problem $T-\psi$ method nodal elements convergence and error estimates.