J. P. Moitinho de Almeida, O. J. B. Almeida Pereira
When local quantities are
computed using the principle of virtual work, dual analysis, which provides an
upper bound of the global error, may also be applied to the virtual problem.
Greenberg and Washizu proposed alternative approaches to combine the global
error bounds of the real and virtual problems, providing upper bounds of the
local error. It is shown in this paper that optimising Greenberg's approach
corresponds to using Washizu's approach, which, in turn, may be further
improved. These approaches are used to provide finite element error indicators
for adaptive refinement.
Keywords: Local quantities;
Error estimation; Dual analysis; Adaptive refinement; Verification