Convergence of a B-E based finite element method for MHD models on Lipschitz domains

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:368

Article

Hu, Kaibo¹  Qiu, Weifeng²  Shi, Ke³ 

[1] Univ Minnesota, Sch Math, Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA

[2] City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Hong Kong, Peoples R China

[3] Old Dominion Univ, Dept Math & Stat, Norfolk, VA 23529 USA

关键词: Magnetohydrodynamics;    Finite element method;    Structure-preserving;    de Rham complex;   

DOI  :  10.1016/j.cam.2019.112477

来源: Elsevier

【 摘 要 】

We discuss a class of magnetic-electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a key L-3 estimate for divergence-free finite element functions for a new type of boundary conditions. With this estimate and a similar one in Hu and Xu (2018), we rigorously prove the convergence of Picard iterations and the finite element schemes with weak regularity assumptions. These results demonstrate the convergence of the finite element methods for singular solutions. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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