Abstract: We considered the finite volume element methods (FVM) based on circumcenter dual subdivision for the elliptic equations and parabolic equations. Let the primal triangular partition satisfy the restrictive condition, that is, the distances between the barycenter Q and the circumcenter C of any triangle element satisfy |QC|=O(h²), under this condition, firstly we have obtained the optimal L² error estimates of the finite volume element method based on circumcenter dual subdivision for the elliptic equation, furthermore we have also proved the optimal L² and H¹ error estimates of the semi-discrete and fully-discrete finite volume element method based on circumcenter dual subdivision for parabolic equation.

Key words: triangular subdivision, dual subdivision, finite volume element method, error estimate