, Volume 104, Issue 2, pp 129-150
Date: 12 Jul 2006

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

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Abstract

Optimal order error estimates in H 1, for the Q 1 isoparametric interpolation were obtained in Acosta and Durán (SIAM J Numer Anal37, 18–36, 1999) 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 cannot 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 π, independently of the aspect ratio. We also show that the restriction on the maximum angle is sharp for p  ≥  3.