A space-time least-square finite element scheme for advection-diffusion equations

A space-time least-square finite element scheme is presented for the advection-diffusion problems at moderate to high Peclet numbers. This scheme is designed to eliminate spurious oscillations and can be used to define the steady-state solution as the asymptotic transient solution for large time. Numerical results, using linear elements in a 1D space and bilinear elements in a 2D space, demonstrate the accuracy and the stability of the new scheme.