A New Stabilized Finite Element Method for Solving the Advection-Diffusion Equations

Abstract

This paper is devoted to the development of a new stabilized finite element method for solving the advection-diffusion equations having the form $-\kappa\Delta u+\underline{a}\bullet\underline{\nabla}u+\sigma u=f$ with a zero Dirichlet boundary condition. We show that this methodology is coercive and has a uniformly optimal convergence result for all mesh-Peclet number.