Erath, C., Gantner, G., & Praetorius, D. (2020). Optimal convergence behavior of adaptive FEM driven by simple (h − h/2)-type error estimators. Computers and Mathematics with Applications, 79(3), 623–642. https://doi.org/10.1016/j.camwa.2019.07.014
Modeling and Simulation; Computational Mathematics; Computational Theory and Mathematics; local mesh-refinement; adaptive algorithm; finite element method; a posteriori error estimators; optimal convergence rates.
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Abstract:
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.
