The Finite Element Approximation For The Two-order Mixed Elliptic Problem And Stokes Problem

In this paper,we study the finite element approximation of the two-order mixed elliptic problem,Stokes problem,and the singular perturbation problem of Darcy-Stokes.We construct a Mini triangular prism element,which is well-posed for the two-order mixed elliptic problem.The discrete B-B condition holds for the element by using Falk-Osborn method.The finite element error estimate results are obtained.Two elements are constructed for the Stokes problem,the Mini triangular prism element and Bernardi-Raugel triangular prism element are included.They are well-posed for the Stokes problem.The discrete B-B condition holds for the elements by using Fortin formula,and the finite element error estimate results are obtained respectively.Two nonconforming elements are constructed for the singular perturbation problem of Darcy-Stokes,the tetrahedron element and the cuboid element are included,theirs posedness are proven.The discrete B-B condition holds for the elements,and two-order convergent results are given respectively.