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

Kaibo Hu; Weifeng Qiu; Ke Shi

doi:10.1016/j.cam.2019.112477

Author(s)

Kaibo Hu
Weifeng Qiu
Ke Shi

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Article number	112477
Journal / Publication	Journal of Computational and Applied Mathematics
Volume	368
Online published	14 Oct 2019
Publication status	Published - Apr 2020

Link(s)

DOI	DOI https://doi.org/10.1016/j.cam.2019.112477 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-85073497969&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(2cb85f93-f7f6-4e87-84be-85dd4bb1ceb5).html

Abstract

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 L³ 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.

Research Area(s)

de Rham complex, Finite element method, Magnetohydrodynamics, Structure-preserving

Citation Format(s)

[ RIS ] [ BibTeX ]

Convergence of a B-E based finite element method for MHD models on Lipschitz domains. / Hu, Kaibo; Qiu, Weifeng; Shi, Ke.

In: Journal of Computational and Applied Mathematics, Vol. 368, 112477, 04.2020.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Hu, K, Qiu, W & Shi, K 2020, 'Convergence of a B-E based finite element method for MHD models on Lipschitz domains', Journal of Computational and Applied Mathematics, vol. 368, 112477. https://doi.org/10.1016/j.cam.2019.112477

Hu, K., Qiu, W., & Shi, K. (2020). Convergence of a B-E based finite element method for MHD models on Lipschitz domains. Journal of Computational and Applied Mathematics, 368, [112477]. https://doi.org/10.1016/j.cam.2019.112477

Hu K, Qiu W, Shi K. Convergence of a B-E based finite element method for MHD models on Lipschitz domains. Journal of Computational and Applied Mathematics. 2020 Apr;368:112477. Epub 2019 Oct 14. doi: 10.1016/j.cam.2019.112477

Hu, Kaibo ; Qiu, Weifeng ; Shi, Ke. / Convergence of a B-E based finite element method for MHD models on Lipschitz domains. In: Journal of Computational and Applied Mathematics. 2020 ; Vol. 368.