Abstract: As is well-known, the solution of Maxwell equations is singular in the sense that the solution does not belong to $H^1(\Omega)$-space. It has been a challenging issue if the Lagrange nodal-continuous finite element method, which is $H^1(\Omega)$-conforming, is suitable for solving such singular solution. In this talk, I talk about how to use the nodal-continuous finite element method to solve Maxwell equations. Source and eigenvalue problems are studied in homogeneous or inhomogeneous media. Theoretical results are presented, together with a number of numerical results. Consequently, our Lagrange finite element method have been theoretically and numerically confirmed to well and correctly solve the singular solutions.
