Nonconforming Mixed Finite Element Method for the Stationary Conduction-Convection Problem

Abstract

In this paper, a new stable nonconforming mixed finite element scheme is proposed for the stationary conduction-convection problem, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken as approximation space for the velocity, the piecewise constant element for the pressure and the bilinear element for the temperature, respectively. The convergence analysis is presented and the optimal error estimates in a broken $H^1$-norm for the velocity, $L^2$-norm for the pressure and $H^1$-seminorm for the temperature are derived.