The finite-element-based lattice Boltzmann scheme for the computations on unstructured meshes is proposed. The scheme is based on the weighted residuals method with Galerkin approximation. The scheme is reduced to the solution of the linear algebraic system at every time step. The possibilities of application of the developed scheme for practical problems are demonstrated on the applications to two test problems of computational fluid dynamics. The investigation of the equilibrium boundary conditions for distribution functions is performed. The obtained results demonstrate that this type of boundary conditions can produced a results which are in good agreement with the results obtained from the solution of hydrodynamical equations at Re ≥ 20. The algorithm of the proposed scheme is realized in GNU license software freefem++ v.3.20.