Résumé
In this paper, we introduce and analyze an a posteriori error estimator for the immersed boundary finite element method called Phi-FEM in the case of the Poisson-Dirichlet equation. The Phi-FEM scheme used a description of the domain by a level-set function. The proposed estimator is based on the residual of the governing equations and a measure of the geometry error quantified thanks to an estimation of the level-set discretization error. We prove the global reliability of this estimator up to oscillation terms linked to the discretization of the boundary and the source term. We validate this estimator through various test cases. Its efficiency and ability to identify regions of high error and guide adaptive strategies are also investigated. Additionally, the paper compares the performance of the proposed a posteriori estimator against the standard FEM one.