Optimal convergence behavior of adaptive FEM driven by simple (h-h/2)-type error estimators
arXiv:1805.0071522 citationsh-index: 34
AI Analysis
Provides theoretical justification for a simple, practical error estimator in adaptive FEM, though limited to specific model problems.
Proved that adaptive FEM using (h-h/2)-type error estimators achieves optimal algebraic convergence rates for Poisson-type problems, with guaranteed lower bounds and efficiency constant 1.
For some Poisson-type model problem, we prove that adaptive FEM driven by the (h-h/2)-type error estimators from [Ferraz-Leite, Ortner, Praetorius, Numer. Math. 116 (2010)] leads to convergence with optimal algebraic convergence rates. Besides the implementational simplicity, another striking feature of these estimators is that they can provide guaranteed lower bounds for the energy error with known efficiency constant 1.