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Volume 22, Issue 5
Convergence of an Alternating A-$\phi$ Scheme for Quasi-Magnetostatics Eddy Current Problem

Changfeng Ma

J. Comp. Math., 22 (2004), pp. 661-670.

Published online: 2004-10

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  • Abstract

We propose in this paper an alternating A-$\phi$ method for the quasi-magnetostatic eddy current problem by means of finite element approximations. Bounds for continuous and discrete error in finite time are given. And it is verified that provided the time step $\tau$ is sufficiently small, the proposed algorithm yields for finite time $T$ an error of $O(h+\tau^{1/2})$ in the $L^2$-norm for the magnetic field $H(= \mu^{-1} \nabla \times A)$, where $h$ is the mesh size, $\mu$ the magnetic permeability.

  • Keywords

Eddy current problem, Alternating $A-\phi$ method, Finite element approximation, Error estimate.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-661, author = {Ma , Changfeng}, title = {Convergence of an Alternating A-$\phi$ Scheme for Quasi-Magnetostatics Eddy Current Problem}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {5}, pages = {661--670}, abstract = {

We propose in this paper an alternating A-$\phi$ method for the quasi-magnetostatic eddy current problem by means of finite element approximations. Bounds for continuous and discrete error in finite time are given. And it is verified that provided the time step $\tau$ is sufficiently small, the proposed algorithm yields for finite time $T$ an error of $O(h+\tau^{1/2})$ in the $L^2$-norm for the magnetic field $H(= \mu^{-1} \nabla \times A)$, where $h$ is the mesh size, $\mu$ the magnetic permeability.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8865.html} }
TY - JOUR T1 - Convergence of an Alternating A-$\phi$ Scheme for Quasi-Magnetostatics Eddy Current Problem AU - Ma , Changfeng JO - Journal of Computational Mathematics VL - 5 SP - 661 EP - 670 PY - 2004 DA - 2004/10 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8865.html KW - Eddy current problem, Alternating $A-\phi$ method, Finite element approximation, Error estimate. AB -

We propose in this paper an alternating A-$\phi$ method for the quasi-magnetostatic eddy current problem by means of finite element approximations. Bounds for continuous and discrete error in finite time are given. And it is verified that provided the time step $\tau$ is sufficiently small, the proposed algorithm yields for finite time $T$ an error of $O(h+\tau^{1/2})$ in the $L^2$-norm for the magnetic field $H(= \mu^{-1} \nabla \times A)$, where $h$ is the mesh size, $\mu$ the magnetic permeability.

Ma , Changfeng. (2004). Convergence of an Alternating A-$\phi$ Scheme for Quasi-Magnetostatics Eddy Current Problem. Journal of Computational Mathematics. 22 (5). 661-670. doi:
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