The accurate calculation of the electromagnetic field enhancement around nanopar- ticles that exhibit facets with small angles is of interest to characterize their efficiency, given the experimental reproducibility of such structures. The finite element method is efficient to com- pute the enhancement of the field intensity at the surface of nanoparticles although the numerical results strongly depends on the mesh of the domain. An adaptive remeshing method is shown to be robust where the classical refinement method fails. The adaptive refinement method uses a posteriori error estimator with interpolation method of the physical field of interest, based on the residual method. The strategy of this method is to remesh the domain of calculation on the basis of the map of the physical and geometrical size that will ensure compliance with the initial geometry and the accuracy of the physical solution. The numerical application shows that the intensity enhancement computed near the vertex between facets with small angles (5◦ ) can reach 23%.