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 Hölder
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 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 Hölder
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 Hölder
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 = {2019-06-17T14:25:24.000+0200},
author = {Nochetto, Ricardo H. and Siebert, Kunibert G. and Veeser, Andreas},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/219a0f381265de00f2cb2b793d95fadd4/britsteiner},
doi = {10.1007/s00211-002-0411-3},
interhash = {485fe501cb1496c4cbf0e564799a304f},
intrahash = {19a0f381265de00f2cb2b793d95fadd4},
journal = {Numerische Mathematik},
keywords = {ians imported vorlaeufig},
language = {English},
number = 1,
owner = {kohlsk},
pages = {163-195},
timestamp = {2019-06-17T12:34:15.000+0200},
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
}