Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system | Zendy

Creusé Emmanuel | Zendy; Nicaise Serge | Zendy; Tang Zuqi | Zendy

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Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system

Author(s) -

Creusé Emmanuel,

Nicaise Serge,

Tang Zuqi

Publication year - 2014

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.3104

Subject(s) - helmholtz equation , a priori and a posteriori , helmholtz free energy , domain decomposition methods , estimator , mathematics , finite element method , boundary (topology) , boundary value problem , maxwell's equations , residual , mathematical analysis , decomposition method (queueing theory) , physics , algorithm , statistics , philosophy , epistemology , quantum mechanics , thermodynamics

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 A ‐formulation, for which the reliability can be established. Numerical tests confirm the obtained theoretical predictions. Copyright © 2014 John Wiley & Sons, Ltd.

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