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?
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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.
I will give an explanation applicable to adaptive mesh refinement (AMR).
An "error indicator" method uses the existing solution for a given mesh to estimate the error incurred by using that mesh. For example, to determine whether a particular region in the mesh needs to be refined, you can use the solutions at adjacent nodes to calculate the derivative (i.e., jump) at the region interfaces. If the jump exceeds some given criteria, then the mesh at those interfaces should be refined.
An "error estimator" method re-generates the solution using a finer mesh then estimates the error of the original mesh given the new refined solution. This method is more accurate than the "error indicator" method but it obviously involves more effort (computational work) to do.