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The aim of this paper is to show that, for any $p \in [1,\infty)$, the$W^{1,p}$-anisotropic interpolation error estimate holds on quadrilateralisoparametric elements verifying the maximum angle condition ($MAC$) and theproperty of comparable lengths for opposite sides ($clos$), i.e., on all thosequadrilaterals with interior angles uniformly bounded away from $\pi$ and withboth pairs of opposite sides having comparable lengths.  For rectangular elements our interpolation error estimate agrees with theusual one whereas for perturbations of rectangles (the most generalquadrilateral elements previously considered as far as we know) our result hassome advantages with respect to the pre-existing ones: the interpolation errorestimate that we proved is written by using two neighboring sides of theelement instead of the sides of the unknown perturbed rectangle and, on theother hand, conditions $MAC$ and $clos$ are much simpler requirements to verifyand with a clearer geometrical sense than those involved in the definition ofperturbations of a rectangle.

Anisotropic interpolation error estimate for arbitrary quadrilateral isoparametric elements