TY - JOUR
T1 - Convergence Analysis of Finite Element Approximation for 3-D Magneto-Heating Coupling Model
AU - Wang , Lixiu
AU - Yao , Changhui
AU - Zhang , Zhimin
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 1
EP - 23
PY - 2020
DA - 2020/02
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/13637.html
KW - Magneto-heating model, finite element methods, nonlinear, solvability, convergent analysis.
AB - <p style="text-align: justify;">In this paper, the magneto-heating model is considered, where the nonlinear terms
conclude the coupling magnetic diffusivity, the turbulent convection zone, the flow fields, ohmic
heat, and α-quench. The highlights of this paper consist of three parts. Firstly, the solvability
of the model is derived from Rothe&#39;s method and Arzela-Ascoli theorem after setting up the
decoupled semi-discrete system. Secondly, the well-posedness for the full-discrete scheme is arrived
and the convergence order $O$($h$<sup>min{$s$,$m$}</sup>+$τ$) is obtained, respectively, where the approximation
scheme is based on backward Euler discretization in time and Nédélec-Lagrangian finite elements
in space. At last, a numerical experiment demonstrates the expected convergence.</p>