Depending on their sizes, dust grains store more or less charges, catalyse more or less chemical reactions, intercept more or less photons and stick more or less efficiently to form embryos of planets. Hence, the need for an accurate treatment of dust coagulation and fragmentation in numerical modelling. However, existing algorithms for solving the coagulation equation are overdiffusive in the conditions of 3D simulations. We address this challenge by developing a high-order solver based on the discontinuous Galerkin method. This algorithm conserves mass to machine precision and allows to compute accurately the growth of dust grains over several orders of magnitude in size with a very limited number of dust bins.