Abstract

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/hKc0 > 0 is not satisfied, where hK 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 L2‐norm are given. Furthermore, we give a Poincaré inequality on a trapezoid which improves a result of Ženišek.

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