Monotone schemes for convection–diffusion problems with convective transport in different forms

Convective transport in convection–diffusion problems can be formulated differently. Convective terms are commonly written in nondivergent or divergent form. For problems of this type, monotone and stable schemes in Banach spaces are constructed in uniform and integral norms, respectively. Monotonicity is related to row or column diagonal dominance. When convective terms are written in symmetric form (the half-sum of the nondivergent and divergent forms), the stability is established in Hilbert spaces of grid functions. Diagonal dominance conditions are given that ensure the monotonicity of two-level schemes for time-dependent convection–diffusion equations and the stability in corresponding spaces.