Generally speaking, a parabolic problem conserves nonnegativity if nonnegative input data lead to a nonnegative solution. This property of the mathematical model is important in physics if we deal with absolute temperature, concentration, density etc. The well-known comparison principle guarantees that the homogeneous linear parabolic problem with homogeneous Dirichlet boundary condition has nonnegative solution for any nonnegative initial condition. It is shown that the standard semidiscretization of this problem, namely the method of lines combined with the first order finite element method, does not conserve nonnegativity
