Abstract
We consider the solution of a system of linear algebraic equations which is obtained from a Raviart-Thomas mixed finite element formulation of Darcy's equations. In [C. E. Powell and D. Silvester, SIAM J. Matrix Anal. Appl., 25 (2003), pp. 718-738], Powell and Silvester developed a block-diagonal preconditioner for this system. In this research work, we extend their results by constructing a block-triangular preconditioner and establish an eigenvalue bound for the preconditioned matrix. The preconditioned matrix is nonsymmetric but it is self-adjoint in a nonstandard inner product. The Bramble-Pasciak-type conjugate gradient method is used to solve the linear system which ensures that the norm of the error is minimized. Numerical experiments confirm the theoretical results and illustrate good convergence properties.