Abstract: The present paper deals with a finite volume element method of the parabolic equations based on triangle subdivision and BB dual sub divisions. The trial space is the piecewise linear functions on triangular meshes, the test space is the piecewise constants corresponding to BB dual subdivisions. Optimal L² and H¹ convergence rates for semi-discrete and fully discrete methods are proved.

Key words: parabolic equation, triangle subdivision, dual subdivis ion, finite volume element method, error estimate