Segmented Lanczos-Chebyshev reduction method for convection dominated flows

It has been noted repeatedly in computational fluid mechanics literature that upwind-facing “essential” boundary condition poses difficulty for the Galerkin finite element method (and central difference method). Essentially three main remedies have been proposed to correct the spurious “wiggles” which may appear under these circumstances: mesh refinement, alternative numerical formulations, and special boundary layer treatment 1].Here, we seek an alternative formulation which has the same effect as special boundary layer functions based on piecewise polynomial solution via the segmented Lanczos-Chebyshev reduction method.