(A) new mixed finite element space over skew hexahedral grids

Abstract

The mixed finite element method has an advantage of finding the approximate pressure and velocity simultaneously. In order to use the mixed finite element method, we construct finite dimensional space of H(div;Ω) and $L^2$ (Ω), respectively. In general, we use triangular grids and rectangular grids for constructing the finite dimensional space in two dimension and use tetrahedral grids and hexahedral grids in three dimension. But we consider a new grid in three dimension that is called a skew hexahedral grid. In this paper, we introduce a new finite element and the finite dimensional space $V_h \times W_h$ of H(div;Ω) $\times L^2$(Ω).