In the present work there are discussed possibilities to solve problems of mathematical physics on unstructured grids. The emphasis is on approximation of the convectiondiffusion equation as the most important application. The main attention is given to constructing difference schemes on triangular grids (as the most general unstructured grids). Approximations on the grids designed via the Delaunay triangulation are highlighted as the most optimal. The basis for constructing discrete analogs is the balance method (integro-interpolation approach) which in publications in English is referred to as the finite volume method. Positive features of this approach are very attractive in case of unstructured grids. For the Delaunay triangulation we have Voronoi cells as control volumes.