In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H1-condition number of preconditioned operator Bh-1Ah is uniformly bounded and its Bh-singular values cluster in a positive finite interval, where Ah is the equivalent nonconforming element discretization of nonselfad joint and indefinite second order elliptic operator A, Bh is usual noncon forming element discretization of selfadjoint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of Bh-1 is given.
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