A finite volume convergence theory for the fast adaptive composite grid methods

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The fast adaptive composite grid method (FAC) is an efficient multilevel technique for adaptive solution of partial differential equations. Most existing FAC convergence theory assumes that the discrete equations and interlevel transfers are variational, which restricts applicability primarily to Galerkin finite element discretizations of self-adjoint elliptic equations. This paper extends the variational two-level theory to the case that the so-called finite volume element scheme is used for discretization.