The relationship of some a posteriori estimators (Q1818507)

In the case of a boundary value problem, an error estimator is usually of residual type (it is computed by using the residual of the finite element solution explicitly or implicitly) or of recovery type (it is computed by locally constructing an improved solution from the finite element approximation). The paper investigates the relationship of the recovery error estimator and the implicit error estimator. It shows analytically that for one-dimensional problems the recovery error estimator involving local residual is equivalent to the implicit residual error estimator. It also provides numerical evidence to demonstrate that such equivalence also exist for two-dimensional problems.