The director structure of a nematic liquid crystal cell containing a surface relief grating has been modelled using a finite element method. Homeotropic alignment is used, with weak anchoring and the flexoelectric term at the grating surface. The diffraction behaviour of the cell has been modelled using the Finite-Difference Time-Domain (FDTD) method. The liquid crystal's response depends on the sign of the applied electric field and gives different increases in diffraction strength in each case. The changes in the diffraction intensity depend on the surface anchoring and flexoelectric coefficients. Experimental results for cells with a similar structure to those modelled show that the variation of diffraction strength with electric fields of different signs is clearly observable. Results obtained by applying pulses to the cells are presented. These results are compared with the theoretical predictions and are used to estimate the surface anchoring and flexoelectric coefficients.