On the sign-stability of numerical solutions of one-dimensional parabolic problems

The preservation of the qualitative properties of physical phenomena in numerical models of these phenomena is an important requirement in scientific computations. In this paper, the numerical solutions of a one-dimensional linear parabolic problem are analysed. The problem can be considered as a altitudinal part of a split air pollution transport model or a heat conduction equation with a linear source term. The paper is focussed on the so-called sign-stability property, which reflects the fact that the number of the spatial sign changes of the solution does not grow in time. We give sufficient conditions that guarantee the sign-stability both for the finite difference and the finite element methods.