A Kind Of Mixed Finite Element Method In H(div, Ω) And Its Applications In Composite Materials With Small Periodic Coefficients

A kind of non C0 and conforming mixed finite element method is given to solve the 2nd order elliptic mixed variational problem with the Dirichlet boundary condition and the elliptic boundary value problem of composite materials with small periodic coefficientsAt the same time, two approximating spaces used in the scheme are satisfied with BB conditions. A convergence theorem is obtained by analyzing the algorithm, which illustrate that the error orders of the two approximating spaces are the same. In this process, the interpolation error orders are avoided the loss and achieve the optimal approximation. Four representative examples are given to verify the results in theory.