We consider a finite element method for the elliptic obstacle problem
over polyhedral domains in R^d , which enforces the unilateral constraint
solely at the nodes. We derive novel optimal upper and lower a posteriori
error bounds in the maximum norm irrespective of mesh fineness and
the regularity of the obstacle, which is just assumed to be H�lder
continuous. They exhibit optimal order and localization to the non-contact
set. We illustrate these results with simulations in 2d and 3d showing
the impact of localization in mesh grading within the contact set
along with quasi-optimal meshes.
%0 Journal Article
%1 nochetto2003pointwise
%A Nochetto, Ricardo H.
%A Siebert, Kunibert G.
%A Veeser, Andreas
%D 2003
%J Numerische Mathematik
%K from:mhartmann ians imported vorlaeufig
%N 1
%P 163-195
%R 10.1007/s00211-002-0411-3
%T Pointwise A Posteriori Error Control for Elliptic Obstacle Problems
%U http://dx.doi.org/10.1007/s00211-002-0411-3
%V 95
%X We consider a finite element method for the elliptic obstacle problem
over polyhedral domains in R^d , which enforces the unilateral constraint
solely at the nodes. We derive novel optimal upper and lower a posteriori
error bounds in the maximum norm irrespective of mesh fineness and
the regularity of the obstacle, which is just assumed to be H�lder
continuous. They exhibit optimal order and localization to the non-contact
set. We illustrate these results with simulations in 2d and 3d showing
the impact of localization in mesh grading within the contact set
along with quasi-optimal meshes.
@article{nochetto2003pointwise,
abstract = {We consider a finite element method for the elliptic obstacle problem
over polyhedral domains in R^d , which enforces the unilateral constraint
solely at the nodes. We derive novel optimal upper and lower a posteriori
error bounds in the maximum norm irrespective of mesh fineness and
the regularity of the obstacle, which is just assumed to be H�lder
continuous. They exhibit optimal order and localization to the non-contact
set. We illustrate these results with simulations in 2d and 3d showing
the impact of localization in mesh grading within the contact set
along with quasi-optimal meshes.},
added-at = {2018-07-20T10:54:36.000+0200},
author = {Nochetto, Ricardo H. and Siebert, Kunibert G. and Veeser, Andreas},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/219a0f381265de00f2cb2b793d95fadd4/mathematik},
doi = {10.1007/s00211-002-0411-3},
interhash = {485fe501cb1496c4cbf0e564799a304f},
intrahash = {19a0f381265de00f2cb2b793d95fadd4},
journal = {Numerische Mathematik},
keywords = {from:mhartmann ians imported vorlaeufig},
language = {English},
number = 1,
owner = {kohlsk},
pages = {163-195},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {Pointwise A Posteriori Error Control for Elliptic Obstacle Problems},
url = {http://dx.doi.org/10.1007/s00211-002-0411-3},
volume = 95,
year = 2003
}
