Abstract: Preconditioners for GMRES method are discussed in solving linear systems discretized from scalar elliptic partial differential equations of second order with jump coeffcient.Based on hierarchical basis,spectral equivalence is established for two kinds of stiffness matrices from quadratic finite element and second order mixed-type finite volume element method,respectively.A preconditioner is proposed by combining equivalence with two-level geometric-algebraic multigrid(GAMG) method which was especially designed for linear systems arising from quadratic finite element discretization.Numerical results confirm correctness of our theoretical analysis.It shows that the preconditioner is quite effcient and robust.

Key words: preconditioner, AMG method, finite volume element method, finite element method