Abstract
In this paper we study the C0 interior penalty method for a quad-curl problem arising from magnetohydrodynamics model on bounded polygons or polyhedrons. We prove the well-posedness of the numerical scheme and then derive the optimal error estimates in a discrete energy norm. A post-processing procedure that can produce C1 approximations is also presented. The performance of the method is illustrated by numerical experiments.
Highlights
The magnetohydrodynamics (MHD) model [1, 11] has wide range of applications in plasma physics, astrophysics, magnetospheric and thermonuclear fusion
The error estimate for the C0 interior penalty (C0-IP) method is given in the following theorem, which directly follows from Lemma 7 and Lemma 8
We developed the C0 interior penalty method for solving the quad-curl problem which arises in the MHD model
Summary
Zhengjia Suna, Fuzheng Gaob, Chao Wangc and Yi Zhangd aCollege of Economics, Shenzhen University Shenzhen, Guangdong 518060, China bSchool of Mathematics, Shandong University Jinan, Shandong 250100, China cDepartment of Applied Mathematics, The Hong Kong Polytechnic University Kowloon, Hong Kong, China dDepartment of Mathematics and Statistics, The University of North Carolina at Greensboro
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