Distinction between error estimator and error indicator

Question

When solving differential equations numerically one can incur discretization error and one can construct a posteriori error estimates to approximate the true error. There is a distinction often made between "error estimators" and "error indicators". What is the difference between the two?

Answer 1

I received an answer from Dr. Klaus-Jurgen Bathe of MIT via email.

"It is probably best to call an indicator simply a measure to indicate the error( like the jumps in stress bands), i.e. nothing strict,whereas the estimator gives a mathematical strict estimate. But other researchers may use the terminology differently"

This does follow the general notion that error indicators are local (element wise) estimations. They are often used to drive AMR routines than precise error estimation.