A guaranteed equilibrated error estimator for the $\mathbf{A}-\varphi$ and $\mathbf{T}-\Omega$ magnetodynamic harmonic formulations of the Maxwell system. (27th June 2016)

• Record Type: Journal Article
• Authors: Creusé, Emmanuel; Nicaise, Serge; Tittarelli, Roberta
• Is Part Of: IMA journal of numerical analysis. Volume 37:Number 2(2017)
• Page Start: 750
• Page End: 773
• Publication Date: 2016-06-27
• Subjects: Maxwell equations -- potential formulation -- a posteriori estimators -- finite element method.; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drw026
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract : In this article, a guaranteed equilibrated error estimator is proposed for the harmonic magnetodynamic formulation of the Maxwell's system. This system is recast into two classical potential formulations, which are solved by a finite element method. The equilibrated estimator is built starting from these dual problems, and is consequently available to estimate the error of both numerical approximations. The estimator's reliability and efficiency without generic constants are established. Then, numerical tests are performed, allowing to illustrate the obtained theoretical results.