Convergence of Finite Elements Adapted for Weaker Norms
P. Morin, K. Siebert, and A. Veeser. Applied and Industrial Matematics in Italy - II, volume 75 of Series on Advances in Mathematics for Applied Sciences, page 468-479. Hackensack, NJ, World Sci. Publ., (2007)
DOI: 10.1142/9789812709394_0041
Abstract
We consider finite elements that are adapted to a (semi)norm that
is weaker than the one of the trial space. We establish convergence
of the finite element solutions to the exact one under the following
conditions: refinement relies on unique quasi-regular element subdivisions
and generates locally quasi-uniform grids; the finite element spaces
are conforming, nested, and satisfy the inf-sup condition; the error
estimator is reliable and appropriately locally efficient; the indicator
of a non-marked element is bounded by the estimator contribution
associated with the marked elements, and each marked element is subdivided
at least once. This abstract convergence result is illustrated by
two examples.
%0 Conference Paper
%1 morin2007convergence
%A Morin, Pedro
%A Siebert, Kunibert G.
%A Veeser, Andreas
%B Applied and Industrial Matematics in Italy - II
%C Hackensack, NJ
%D 2007
%E Cutello, V.
%E Fotia, G.
%E Puccio, L.
%I World Sci. Publ.
%K Adaptivity; conforming convergence elements; finite from:mhartmann ians vorlaeufig
%P 468-479
%R 10.1142/9789812709394_0041
%T Convergence of Finite Elements Adapted for Weaker Norms
%U http://dx.doi.org/10.1142/9789812709394_0041
%V 75
%X We consider finite elements that are adapted to a (semi)norm that
is weaker than the one of the trial space. We establish convergence
of the finite element solutions to the exact one under the following
conditions: refinement relies on unique quasi-regular element subdivisions
and generates locally quasi-uniform grids; the finite element spaces
are conforming, nested, and satisfy the inf-sup condition; the error
estimator is reliable and appropriately locally efficient; the indicator
of a non-marked element is bounded by the estimator contribution
associated with the marked elements, and each marked element is subdivided
at least once. This abstract convergence result is illustrated by
two examples.
%Z Selected Contributions from the 8th SIMAI Conference
@inproceedings{morin2007convergence,
abstract = {We consider finite elements that are adapted to a (semi)norm that
is weaker than the one of the trial space. We establish convergence
of the finite element solutions to the exact one under the following
conditions: refinement relies on unique quasi-regular element subdivisions
and generates locally quasi-uniform grids; the finite element spaces
are conforming, nested, and satisfy the inf-sup condition; the error
estimator is reliable and appropriately locally efficient; the indicator
of a non-marked element is bounded by the estimator contribution
associated with the marked elements, and each marked element is subdivided
at least once. This abstract convergence result is illustrated by
two examples.},
added-at = {2018-07-20T10:54:55.000+0200},
address = {Hackensack, NJ},
annote = {Selected Contributions from the 8th SIMAI Conference},
author = {Morin, Pedro and Siebert, Kunibert G. and Veeser, Andreas},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2fce4e9b014d31fd0d86f38290a10c472/mathematik},
booktitle = {Applied and Industrial Matematics in Italy - II},
doi = {10.1142/9789812709394_0041},
editor = {Cutello, V. and Fotia, G. and Puccio, L.},
interhash = {925adb90742287cf8df2f5f719eaa4d6},
intrahash = {fce4e9b014d31fd0d86f38290a10c472},
keywords = {Adaptivity; conforming convergence elements; finite from:mhartmann ians vorlaeufig},
owner = {kohlsk},
pages = {468-479},
publisher = {World Sci. Publ.},
series = {Series on Advances in Mathematics for Applied Sciences},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {Convergence of Finite Elements Adapted for Weaker Norms},
url = {http://dx.doi.org/10.1142/9789812709394_0041},
volume = 75,
year = 2007
}
