Asymptotically exact a posteriori error estimator for biquadratic elements (Q1090148)

This paper addresses the finite element method with a posteriori error estimation for elements of degree \(p=1\) and \(p=2\). It gives the formulae for the error indicators and error estimators. Basic mathematical characterizations of the estimators are given and it is shown that the estimators for \(p=1\) and \(p=2\) have different structures. Numerical examples show the effectivity of the approach and the high quality of the estimator.