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Volume 12, Issue 4
A $T-ψ$ Finite Element Method for a Nonlinear Degenerate Eddy Current Model with Ferromagnetic Materials

Tong Kang & Tao Chen

Int. J. Numer. Anal. Mod., 12 (2015), pp. 636-663.

Published online: 2015-12

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  • 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.

  • Keywords

nonlinear degenerate eddy current problem, $T-\psi$ method, nodal elements, convergence, and error estimates.

  • AMS Subject Headings

35Q60, 65N30, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-636, author = {Tong Kang and Tao Chen}, title = {A $T-ψ$ Finite Element Method for a Nonlinear Degenerate Eddy Current Model with Ferromagnetic Materials}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/505.html} }
TY - JOUR T1 - A $T-ψ$ Finite Element Method for a Nonlinear Degenerate Eddy Current Model with Ferromagnetic Materials AU - Tong Kang & Tao Chen 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.

Tong Kang and Tao Chen. (2015). A $T-ψ$ Finite Element Method for a Nonlinear Degenerate Eddy Current Model with Ferromagnetic Materials. International Journal of Numerical Analysis and Modeling. 12 (4). 636-663. doi:
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