Preconditioning projection nonconforming element method for the lowest-order Raviart-Thomas mixed triangular element method

This paper is concerned with the H-1-condition number and the B-h-singular value distribution of preconditioned operators {B-h(-1) A(h)}(0<h<1), where A(h) is the projection nonconforming element discretization of the nonself-adjoint and possibly indefinite second order elliptic operator A, B-h is the nonconforming element discretization of the self-adjoint and positive definite second order elliptic operator B. The projection nonconforming element method is equivalent to the lowest-order Raviart-Thomas mixed triangular element method for second order elliptic problems. It is proved that the H-1-condition number of operators {B-h(-1) A(h)}(0<h<1) are uniformly bounded and the B-h-singular values cluster in a positive finite interval. Finally a simple V-cycle multigrid implementation of B-h(-1) is given. (C) 1998 Elsevier Science Inc. All rights reserved.