Optimal convergence behavior of adaptive FEM driven by simple (h−h∕2)-type error estimators

Christoph Erath; Gregor Gantner; Dirk Praetorius

doi:10.1016/j.camwa.2019.07.014

Optimal convergence behavior of adaptive FEM driven by simple (h−h∕2)-type error estimators

Christoph Erath
, Gregor Gantner^*
, Dirk Praetorius

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

13 Citations (Scopus)

Abstract

For some Poisson-type model problem, we prove that adaptive FEM driven by the
(h−h∕2)-type error estimators from Ferraz-Leite et al. (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.

Original language	English
Pages (from-to)	623-642
Number of pages	20
Journal	Computers & mathematics with applications
Volume	79
Issue number	3
Early online date	23 Jul 2019
DOIs	https://doi.org/10.1016/j.camwa.2019.07.014
Publication status	Published - Feb 2020
Externally published	Yes

Keywords

n/a OA procedure
A posteriori error estimators
Adaptive algorithm
Local mesh-refinement
Optimal convergence rates
Finite element method

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10.1016/j.camwa.2019.07.014Licence: Elsevier licence

Cite this

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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 et al. (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.",

keywords = "n/a OA procedure, A posteriori error estimators, Adaptive algorithm, Local mesh-refinement, Optimal convergence rates, Finite element method",

author = "Christoph Erath and Gregor Gantner and Dirk Praetorius",

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AB - For some Poisson-type model problem, we prove that adaptive FEM driven by the (h−h∕2)-type error estimators from Ferraz-Leite et al. (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.

KW - n/a OA procedure

KW - A posteriori error estimators

KW - Adaptive algorithm

KW - Local mesh-refinement

KW - Optimal convergence rates

KW - Finite element method

UR - https://www.scopus.com/pages/publications/85069663716

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DO - 10.1016/j.camwa.2019.07.014

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JO - Computers & mathematics with applications

JF - Computers & mathematics with applications

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ER -

Optimal convergence behavior of adaptive FEM driven by simple (h−h∕2)-type error estimators

Abstract

Keywords

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