In this paper, we analyze the spatially semi-discrete piecewise linear finite volume element method for the time fractional sub-diffusion problem in two dimensions, and give an ap- proximate solution of this problem. At first, we introduce bilinear finite volume element method with interpolated coefficients and derive some error estimates between exact so- lution and numerical solution in both finite element and finite volume element methods. Furthermore, we use the standard finite element Ritz projection and also the elliptic pro- jection defined by the bilinear form associated with the variational formulation of the fi- nite volume element method. Finally, some numerical examples are included to illustrate the effectiveness of the new technique.
