(Higher Normal School of Technological Education-Skikda, 2025) Arif, Raouf; Gouassmia, Mohamed
In this memory we review the basic concepts to obtain a posteriori error estimates for
the finite element solution of an elliptic linear model problem. We give the basic ideas
to establish global error estimates for the energy norm as well as goal-oriented error
estimates. While we show how these error estimation techniques are employed for our
simple model problem, the emphasis of the memory is on assessing whether these procedures
are ready for use in practical linear finite element analysis. We conclude that
the actually practical error estimation techniques do not provide mathematically proven
bounds on the error and need to be used with care. The more accurate estimation procedures
also do not provide proven bounds that, in general, can be computed efficiently.
We also briefly comment upon the state of error estimations in nonlinear and transient
analyses and when mixed methods are used
