Preconditioners for higher order finite element discretizations of H(div)-elliptic problem

Abstract

In this paper, we are concerned with the fast solvers for higher order finite element discretizations of H(div)-elliptic problem. We present the preconditioners for the first family and second family of higher order divergence conforming element equations, respectively. By combining the stable decompositions of two kinds of 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.