Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes

摘要

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 ρK/h_K ≥ c_0 > 0 is not satisfied, where h_K is the diameter of the element K and ρK 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.