Istituto di Matematica Applicata e Tecnologie Informatiche     
Perugia I., Simoncini V. An optimal indefinite preconditioner for a mixed finite element method. Technical report ercim.cnr.ian//1998-1098, 1998.
Mixed finite element methods give rise to large symmetric indefinite linear systems with a highly structured coefficient matrix. When solving such systems with an iterative method, preconditioning is compulsory. In this paper we analyze an indefinite preconditioner for a mixed formulation of the magnetostatic problem and we show its optimality by proving that the eigenvalues of the preconditioned matrix are located in a bounded interval independent of the characteristic dimension of the mesh used in the discretization. In order to cope with possible memory constraints, alternative quasi-optimal preconditioners are also proposed and experiments demonstrating their effectiveness are reported.
Subject Mixed finite element method

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