Analysis of an interior penalty DG method for the quad-curl problem. (13th August 2020)

• Record Type: Journal Article
• Authors: Chen, Gang; Qiu, Weifeng; Xu, Liwei
• Is Part Of: IMA journal of numerical analysis. Volume 41:Number 4(2021)
• Page Start: 2990
• Page End: 3023
• Publication Date: 2020-08-13
• Subjects: mixed finite element method -- quad-curl problem -- Lipschitz domain -- low regularity -- discrete Sobolev imbedding inequality; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/draa034
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: The quad-curl term is an essential part of the resistive magnetohydrodynamic equation and the fourth-order inverse electromagnetic scattering problem, which are both of great significance in science and engineering. It is desirable to develop efficient and practical numerical methods for the quad-curl problem. In this paper we first present some new regularity results for the quad-curl problem on Lipschitz polyhedron domains, and then propose a mixed finite element method for solving the quad-curl problem. With a novel discrete Sobolev imbedding inequality for the piecewise polynomials, we obtain stability results and derive error estimates based on a relatively low-regularity assumption of the exact solution.