Preconditioners for higher order edge finite element discretizations of Maxwell’s equations

Abstract

In this paper, we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell’s equations. We present the preconditioners for the first family and second family of higher order Nedelec element equations, respectively. By combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning, we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids. We also present some numerical experiments to demonstrate the theoretical results.