Finite Element Convergence For The Darwin Model To Maxwell's Equations

. We will derive the H(curl; \Omega\Gamma and H(curl; div;\Omega\Gamma variational formulations for the Darwin model of approximation to Maxwell's equations in three dimensions, and prove the well-posedness of the variational systems. Then Nedelec's and standard finite element methods are used to solve two kinds of variational problems. Though symmetric bilinear forms in the variational systems fail to define full norms equivalent to the standard norms in the finite element subspaces of H(curl; and H(curl; div;\Omega\Gammav we can still prove the finite element convergence and obtain the error estimates, without requiring the physical domains to be convex. 1. Introduction. It is known that there are more and more scientific problems which involve the solutions of Maxwell's equations, e.g., plasma physics, microwave devices, diffraction of electromagnetic waves. In many cases, the numerical resolution of the full system of Maxwell's equations may be very expensive in terms of the com..