Approximation of singular solutions and singular data for Maxwell’s equations by Lagrange elements

Abstract A Lagrange finite element method is proposed for Maxwell’s equations in Lipschitz domains. The suitable the approximation of singular solutions lying outside $(H^1(\varOmega ))^3$, with nonhomogeneous boundary data tangential trace space $H({\mathbf{curl}}; \varOmega )$ and a right-hand-side source term $(H_0({\mathbf{curl}}; ))^{\prime}$ (the dual $H_0({\mathbf{curl}}; ))$. Numerical results are presented to illustrate performance theoretical results.