Combined Hybrid Finite Element Methods for the Poisson Equation

Applying the idea of energy optimization presented by Tian-xiao Zhou to solve the boundary value problem of Poisson equation, the authors present a combined hybrid finite element method, and construct two groups of low-order quadrilateral finite element by using Wilson non-conforming displacement and Taylor non-conforming displacement. Compared to biquadratic element (Q_2), these elements require less degrees of freedom, the computational precision proves to be better in rectangle partition.