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Keywords:

  • adaptive refinement;
  • goal-oriented adaptivity;
  • dual analysis;
  • model verification;
  • error bounds

Abstract

In this paper, we summarize how dual analysis techniques can be used to determine upper bounds of the discretization error, both in terms of global and local outputs. We present formulas for the bounds of the error in local outputs, based on the approach proposed by Greenberg in 1948 and we show that the resulting intervals are the same as those previously presented, based on the approach proposed by Washizu in 1953. We then explain how the elemental contributions to these bounds can be used to define an adaptive strategy that considers multiple quantities and we present its application to a simple plane stress problem. Copyright © 2010 John Wiley & Sons, Ltd.