Summary: Two splitting schemes are proposed for the numerical solution of three-dimensional nonstationary convection-diffusion problems on unstructured meshes in the case of a full diffusion tensor. An advantage of the first scheme is that the splitting is generated by the properties of the approximation spaces and does not reduce the order of accuracy. An advantage of the second scheme is that the resulting numerical solutions are nonnegative. A numerical study is conducted to compare the splitting schemes with classical methods, such as finite elements and mixed finite elements. The numerical results show that the splitting schemes are characterized by low dissipation, high-order accuracy, and versatility.