(untitled) (Journal of Computational Mathematics, 2018)
In this paper, we construct a tetrahedral element named DST20 for the three dimensional Darcy-Stokes problem, which reduces the degrees of velocity in [30]. The finite element space V_h for velocity is H(div)-conforming, i.e., the normal component of a function in V_h is continuous across the element boundaries, meanwhile the tangential component of a function in V_h is average continuous across the element boundaries, hence V_h is H^1-average conforming. We prove that this element is uniformly convergent with respect to the perturbation constant ε for the Darcy-Stokes problem. At the same time, we give a discrete de Rham complex corresponding to DST20 element.