The elementary mechanism of laminar mixing is analyzed with numerical simulation from the point of view of nonlinear dynamical theory. The analyzed flow is a time-periodic cellular convection in the two dimensional plane system. The effect of molecular diffusion is neglected in order to investigate the mechanism of mixing performed only by convection. The mixing processes can be classified into three steps. In the initial stage, the mixing pattern and the fluid exchange between the cells are determined by the geometric shapes of the lobes, which are composed of stable manifolds and unstable manifolds near the cell boundaries. In the next stage, the chaotic motion of fluid plays an important role in the construction of the fine structure in the lobes. The mixing pattern in the final stage is controlled by the geometric shape of the outermost KAM curves in the cells.