Preserving nonnegativity of an affine finite element approximation for a convection-diffusion-reaction problem

An affine finite element scheme approximation of a time dependent linear convectiondiffusion-reaction problem in 2D and 3D is presented. Specific conditions are given in terms of the coefficient functions, the computational grid and the discretization parameters to ensure that the nonnegativity property of the true solution is also satisfied by its approximation. Numerical examples are given which confirm the necessity and sufficiency of the discretization conditions to ensure the nonnegativity of the approximation.