Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible Magnetohydrodynamics equations

被引：6
|
作者：
Qiu, Weifeng [1 ]
Shi, Ke [2 ]
机构：
[1] City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Hong Kong, Peoples R China
[2] Old Dominion Univ, Dept Math & Stat, Norfolk, VA 23529 USA
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 80卷 / 10期
关键词：
Magnetohydrodynamics; Finite element method; Structure-preserving; DENSITY CONSERVATIVE SCHEME; MAGNETIC REYNOLDS-NUMBER; MHD FLOWS; EXTERIOR CALCULUS; APPROXIMATION;
D O I：
10.1016/j.camwa.2020.09.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We revise the structure-preserving finite element method in [K. Hu, Y. MA and J. Xu. (2017) Stable finite element methods preserving del . B = 0 exactly for MHD models. Numer. Math., 135, 371-396]. The revised method is semi-implicit in time-discretization. We prove the linearized scheme preserves the divergence free property for the magnetic field exactly at each time step. Further, we showed the linearized scheme is unconditionally stable and we obtain optimal convergence in the energy norm of the revised method even for solutions with low regularity. (C) 2020 Elsevier Ltd. All rights reserved.
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页码：2150 / 2161
页数：12
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