Volume 17, Issue 1
Convergence Analysis of Finite Element Approximation for 3-D Magneto-Heating Coupling Model
DOI:

Int. J. Numer. Anal. Mod., 17 (2020), pp. 1-23.

Published online: 2020-02

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• Abstract

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 is consist of three parts. Firstly, the solvability of the model is derived from Rothe'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 $O$($h$min{$s$,$m$} + $τ$) 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.

• Keywords

Magneto-heating model, finite element methods, nonlinear, solvability, convergent analysis.

65M60, 65M15, 35Q60, 35B45

lxwang@csrc.ac.cn (Lixiu Wang)

chyao@lsec.cc.ac.cn (Changhui Yao)

zmzhang@csrc.ac.cn (Zhimin Zhang)

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@Article{IJNAM-17-1, author = {Wang , Lixiu and Yao , Changhui and Zhang , Zhimin }, title = {Convergence Analysis of Finite Element Approximation for 3-D Magneto-Heating Coupling Model}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {1}, pages = {1--23}, abstract = {

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 is consist of three parts. Firstly, the solvability of the model is derived from Rothe'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 $O$($h$min{$s$,$m$} + $τ$) 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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13637.html} }
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 -

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 is consist of three parts. Firstly, the solvability of the model is derived from Rothe'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 $O$($h$min{$s$,$m$} + $τ$) 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.

Lixiu Wang, Changhui Yao & Zhimin Zhang. (2020). Convergence Analysis of Finite Element Approximation for 3-D Magneto-Heating Coupling Model. International Journal of Numerical Analysis and Modeling. 17 (1). 1-23. doi:
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