Développement asymptotique et approximation de la solution des équations de Maxwell dans un polygone

We present an improved version of the Singular Complement Method (SCM) for Maxwell's equations, which relies on an asymptotic expansion of the solution near non-regular points. This method allows to recover an optimal error estimate when used with $\mathbb{P}_1$ Lagrange finite elements; extension to higher-degree elements is possible. It can be applied to static, harmonic, or time-dependent problems.