A mortar edge element method with nearly optimal convergence for three-dimensional Maxwell's equations

Abstract

. In this paper, we are concerned with mortar edge element methods for solving three-dimensional Maxwell's equations. A new type of Lagrange multiplier space is introduced to impose the weak continuity of the tangential components of the edge element solutions across the interfaces between neighboring subdomains. The mortar edge element method is shown to have nearly optimal convergence under some natural regularity assumptions when nested triangulations are assumed on the interfaces. A generalized edge element interpolation is introduced which plays a crucial role in establishing the nearly optimal convergence. The theoretically predicted convergence is confirmed by numerical experiments.