A Finite Element algorithm, based on boundary conformal mapping techniques, is developed and applied to investigate the effect of kinetics on crystal growth of garnets from the melt. The anisotropic interfacial kinetic model given here can lead to the formation of facets along the melt/crystal interface. The influence of the maximum deviation angle θ_max in the kinetic model on the interface shape and calculation errors is vestigated. An efficient method to reduce the calculation error is also given, i. e. taking into account the surface tension effects in the model equations.