Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system. (19th February 2014)

• Record Type: Journal Article
• Authors: Creusé, Emmanuel; Nicaise, Serge; Tang, Zuqi
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 4(2015:Mar. 15)
• Page Start: 738
• Page End: 750
• Publication Date: 2014-02-19
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3104
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma3104-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma3104-para-0001">This paper is devoted to the derivation of a Helmholtz decomposition of vector fields in the case ofmixed boundary conditions imposed on the boundary of the domain. This particular decomposition allows to obtain a residual a posteriori error estimator for the approximation ofmagnetostatic problems given in the so‐called <italic>A</italic>‐formulation, for which the reliability can be established. Numerical tests confirm the obtained theoretical predictions. Copyright © 2014 John Wiley &amp; Sons, Ltd.</p> </abstract>