An efficient direct solver for a class of mixed finite element problems

in this paper we present an efficient, accurate and parallelizable direct m ethod for the solution of the (indefinite) linear algebraic systems that ar ise in the solution of fourth-order partial differential equations (PDEs) u sing mixed finite element approximations. The method is intended particular ly for use when multiple right-hand sides occur, and when high accuracy is required in these solutions. The algorithm is described in some detail and its performance is illustrated through the numerical solution of a biharmon ic eigenvalue problem where the smallest eigenpair is approximated using in verse iteration after discretization via the Ciarlet-Raviart mixed finite e lement method. (C) 2001 IMACS. Published by Elsevier Science B.V. All right s reserved.