We derive sharp and explicit upper bounds for possibly weighted Poincaré constants of finite element stars. The latter are star-shaped domains that consist of a finite number of nonoverlapping simplices or parallelepipeds which all share a common vertex. Bounds for Poincaré constants are needed in deriving error estimates for quasi-interpolation operators and a posteriori upper bounds.
Poincaré constants for finite element stars / A. Veeser, R. Verfuerth. - In: IMA JOURNAL OF NUMERICAL ANALYSIS. - ISSN 0272-4979. - 32:1(2012 Jan), pp. 30-47.
Poincaré constants for finite element stars
A. Veeser
;
2012
Abstract
We derive sharp and explicit upper bounds for possibly weighted Poincaré constants of finite element stars. The latter are star-shaped domains that consist of a finite number of nonoverlapping simplices or parallelepipeds which all share a common vertex. Bounds for Poincaré constants are needed in deriving error estimates for quasi-interpolation operators and a posteriori upper bounds.
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