Guaranteed Quantity of Interest Error Estimate Based on Equilibrated Flux Reconstruction

The quality of a local physical quantity obtained by the numerical method, such as the finite element method (FEM), attracts more and more attention in computational electromagnetism. Inspired by the idea of goal-oriented error estimate given for the Laplace problem, this work is devoted to a guaranteed a posteriori error estimate adapted for the quantity of interest (QOI) linked to magnetostatic problems, in particular, to the value of the magnetic flux density. The development is principally based on an equilibrated flux construction, which ensures fully computable estimators without any unknown constant. The main steps of the mathematical development are given in detail with the physical interpretation. An academic example using an analytical solution is considered to illustrate the performance of the approach, and a discussion about different aspects related to the practical point of view is proposed.