On the stable solution of transient convection–diffusion equations

作者：

Highlights：

• 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.

摘要

•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.

论文关键词：Transient convection–diffusion equation,Monotone finite element scheme,Dominating convection,Error estimates for time-dependent problem

论文评审过程：Received 5 September 2013, Revised 30 November 2014, Available online 9 December 2014.

论文官网地址：https://doi.org/10.1016/j.cam.2014.12.001