O. J. B. Almeida Pereira and J. P. Moitinho de Almeida
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.
KEY WORDS: adaptive
refinement; goal-oriented adaptivity; dual analysis; model verification; error bounds.