On the stable solution of transient convection–diffusion equations

• We consider transient convection–diffusion equation with dominating convection.
• The model has an application in optimal control of the asymmetric flow field-flow fractionation process.
• For a stable discretization we propose a monotone edge-averaged finite element (EAFE) scheme.
• EAFE is generalized to a time-dependent case and a new error estimate is proved.
• We present numerical results for comparison with a popular SUPG method.

A transient convection–diffusion equation is considered, which particularly arises in optimization problems for the asymmetric flow field-flow fractionation (AF4) process. A time-dependent generalization of the monotone edge-averaged finite element (EAFE) scheme is used to obtain a stable discretization in the convection-dominated regime. New error estimates are proved for this scheme and a comparison with the popular SUPG method is presented. Numerical experiments demonstrate that the EAFE method is more suitable for problems where boundary layers are formed.