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

Simon Labrunie (1, 2) , Boniface Nkemzi (1)

1 IECN - Institut Élie Cartan de Nancy
2 CALVI - Scientific computation and visualization

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.

Domaines: Equations aux dérivées partielles [math.AP]

Simon Labrunie, Boniface Nkemzi. Développement asymptotique et approximation de la solution des équations de Maxwell dans un polygone. 2006. ⟨hal-00094352⟩