Some Researches On Finite Elements For Aribitrary Narrow Quadrilateral

In this paper, the Poincar?inequality on trapezoid with a right angle is discussed, and the constant is specified. Extended the results to three ?dimensional space, the Poincar?inequality on unit cube and trapezoid platform with a right angle is studied, and the upper bound of the constant is obtained. Then, in the case of non ?regularity meshes, the rectangular el- ements for arbitrary narrow rectangular are discussed. Some com- mon rectangular elements are tested whether they satisfy the condi- tion Or not. Using the anisotropic interpolation theorems for narrow quadrilateral finite elements, the interpolation error of the Wilson el- ement for arbitrary narrow rectangular is obtained. With a series of estimates on the reference element, the convergence property of sec- ond order problems is proved without satisfying the regularity condi- tions, and its convergence order equals to the one of regularity mesh- es.