Insight into the flow-condition-based interpolation finite element approach: solution of steady-state advection-diffusion problems

The flow-condition-based interpolation (FCBI) finite element approach is studied in the solution of advection–diffusion problems. Two FCBI procedures are developed and tested with the original FCBI method: in the first scheme, a general solution of the advection–diffusion equation is embedded into the interpolation, and in the second scheme, the link-cutting bubbles approach is used in the interpolation. In both procedures, as in the original FCBI method, no artificial parameters are included to reach stability for high Péclet number flows. The procedures have been implemented for two-dimensional analysis and the results of some test problems are presented. These results indicate good stability and accuracy characteristics and the potential of the FCBI solution approach