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 - <p style="text-align: justify;">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.</p>