Abstract. We propose a method for constructing a continuous piecewise-polynomial weight functions for the Petrov–Galerkin method in three-dimensional domain. The form of the functions is determined by a finite number of variable parameters associated with the edges of the grid partition. It is expected that the choice of these parameters allows obtaining the numerical approximation of the original equation without non-physical oscillations (when saving the sufficient accuracy). The investigation results are illustrated with some test calculations.

Keywords: finite element method, Petrov–Galerkin method, convection–diffusion–reaction equation, three-dimensional case.