The Quasi-Wilson Element For Arbitrary Narrow Quadrilateral

The regularity conditions are essential for the tranditional finite elements. They restrict the application of the elements in a way. In the case of non-regularity meshes, the quasi-Wilson element for arbitrary narrow quadrilateral are studied in this paper. The main results are as follows: 1. By construction of quasi-Wilson element on reference element, we prove that the resulting elements pass through Irons? patch test for arbitrary narrow quadrilateral meshes. 2. Using the interpolation theorems for narrow quadrilateral isoparametric finite elements, the interpolation errors of the quasi- Wilson element for arbitrary narrow quadrilateral are obtained. 3. By a series of estimates on reference element, the convergence property for second order problems are proved without satisfying the regularity conditions, and its convergence order is same as that of regularity meshes. Meanwhile, by the accurate proof of Poincare inequality on reference element, some constants of estimates are given concretely.