Numerische Mathematik

, Volume 104, Issue 2, pp 129–150

Interpolation error estimates in W1,p for degenerate Q1 isoparametric elements

Article

Abstract

Optimal order error estimates in H1, for the Q1 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 W1,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.

AMS Subject Classification

65N15 65N30 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Universidad Nacional De General SarmientoBuenos AiresArgentina

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