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

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.