A new finite element space for expanded mixed finite element method

In this article, we propose a new finite element space ?h for the expanded mixed finite element method (EMFEM) for second-order elliptic problems to guarantee its com-puting capability and reduce the computation cost. The new finite element space ?h is designed in such a way that the strong requirement Vh subset of ?h in [9] is weakened to {vh is an element of Vh; divvh = 0} subset of ?h so that it needs fewer degrees of freedom than its classical counterpart. Furthermore, the new ?h coupled with the Raviart-Thomas space satisfies the inf-sup condition, which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix, and thus the existence, uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in Rd, d = 2, 3 and for triangular partitions in R2. Also, the solvability of the EMFEM for triangular partition in R3 can be directly proved without the inf-sup condition. Numerical experiments are conducted to confirm these theoretical findings.