Interpolation error estimates in W 1,p for degenerate Q1 isoparametric elements

Abstract. Optimal order error estimates in H1, for the Q1 isoparametric interpolation, were obtained in [2] for a very general class of degenerate convex quadrilateral elements. In this work we show that the same conlusions are valid in W 1,p for 1 ≤ p < 3 and we give a counterexample for the case p ≥ 3, showing that the result can not be generalized for more regular functions. Despite this fact, we show that optimal order error estimates are valid for any p ≥ 1, keeping the interior angles of the element bounded away from 0 and pi, independently of the aspect ratio. We also show that the restriction on the maximum angle is sharp for p ≥ 3