A Stabilized Finite Element Method for Non-Stationary Conduction-Convection Problems (Advances in Applied Mathematics and Mechanics, 2018)
This paper is concerned with a stabilized finite element methodbased on two local Gauss integrations for the two-dimensionalnon-stationary conduction-convection equations by using the lowestequal-order pairs of finite elements. This method only offsets thediscrete pressure space by the residual of the simple and symmetryterm at element level in order to circumvent the inf-sup condition.The stability of the discrete scheme is derived under someregularity assumptions. Optimal error estimates are obtained byapplying the standard Galerkin techniques. Finally, the numericalillustrations agree completely with the theoretical expectations.