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

Archive ouverte : Article de revue

Creusé, Emmanuel | Nicaise, Serge | Tang, Zuqi

Edité par HAL CCSD ; Wiley

International audience. This paper is devoted to the derivation of a Helmholtz decomposition of vector fields in the case of mixed boundary conditions imposed on the boundary of the domain. This particular decomposition allows to obtain a residual a posteriori error estimator for the approximation of magnetostatic problems given in the so-called A formulation, for which the reliability can be established. Numerical tests confirm the obtained theoretical predictions.

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