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

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-0 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 7- 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-$\theta$ method Finite element approximation error estimate

@Article{JCM-22-661, author = {}, 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-0 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 7- 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 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 KW - Alternating A-$\theta$ method KW - Finite element approximation KW - error estimate AB - We propose in this paper an alternating A-0 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 7- 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.