Algebraic multilevel iteration method for lowest order Raviart-Thomas space and applications

An optimal order algebraic multilevel iterative method for solving system of linear algebraic equations arising from the finite element discretization of certain boundary value problems, that have their weak formulation in the space H(div), is presented. The algorithm is developed for the discrete problem obtained by using the lowest-order Raviart-Thomas space. The method is theoretically analyzed and supporting numerical examples are presented. Furthermore, as a particular application, the algorithm is used for the solution of the discrete minimization problem which arises in the functional-type a posteriori error estimates for the discontinuous Galerkin approximation of elliptic problems. Copyright (C) 2011 John Wiley & Sons, Ltd.