@Article{CiCP-29-1125,
author = {Chen , HuangxinLi , JingzhiQiu , Weifeng and Wang , Chao},
title = {A Mixed Finite Element Scheme for Quad-Curl Source and Eigenvalue Problems},
journal = {Communications in Computational Physics},
year = {2021},
volume = {29},
number = {4},
pages = {1125--1151},
abstract = {<p style="text-align: justify;">The quad-curl problem arises in the resistive magnetohydrodynamics
(MHD) and the electromagnetic interior transmission problem. In this paper we study
a new mixed finite element scheme using Nédélec&#39;s edge elements to approximate
both the solution and its curl for quad-curl problem on Lipschitz polyhedral domains.
We impose element-wise stabilization instead of stabilization along mesh interfaces.
Thus our scheme can be implemented as easy as standard&nbsp;Nédélec&#39;s methods for
Maxwell&#39;s equations. Via a discrete energy norm stability due to element-wise stabilization, we prove optimal convergence under a low regularity condition. We also
extend the mixed finite element scheme to the quad-curl eigenvalue problem and provide corresponding convergence analysis based on that of source problem. Numerical
examples are provided to show the viability and accuracy of the proposed method for
quad-curl source problem.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0108},
url = {http://global-sci.org/intro/article_detail/cicp/18649.html}
}