P. Ladeveze et N. Moes, A NEW A-POSTERIORI ERROR ESTIMATION FOR NONLINEAR TIME-DEPENDENT FINITE-ELEMENT ANALYSIS, Computer methods in applied mechanics and engineering, 157(1-2), 1998, pp. 45-68
In this paper, an error on the constitutive law (labeled the dissipati
on error) is used to measure the quality of finite element computation
s of plastic and viscoplastic structures whose behavior is described b
y internal variables. This measure takes into account all the classica
l sources of error involved in the computation: the space discretizati
on (the mesh), the time discretization and the iterative technique use
d to solve the nonlinear discrete problem. More specifically, to quant
ify the quality of the space and time discretizations, two quantifies,
called indicators, are introduced. The efficiency of both the error a
nd the indicators is shown for several examples. (C) 1998 Elsevier Sci
ence S.A.