Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes

In this paper an anisotropic interpolation theorem is presented that can be easily used to check the anisotropy of an element. A kind of quasi-Wilson element is considered for second-order problems on narrow quadrilateral meshes for which the usual regularity condition rho(K)/h(K) greater than or equal to c(0) > 0 is not satisfied, where h(K) is the diameter of the element K and rho(K) is the radius of the largest inscribed circle in K. Anisotropic error estimates of the interpolation error and the consistency error in the energy norm and the L-2-norm are given. Furthermore, we give a Poincare inequality on a trapezoid which improves a result of Zenisek.