Besides an algorithm for local refinement, an a posteriori error estimator
is the basic tool of every adaptive finite element method. Using
information generated by such an error estimator the refinement of
the grid is controlled. For 2nd order elliptic problems we present
an error estimator for anisotropically refined grids, like n -d cuboidal
and 3-d prismatic grids, that gives correct information about the
size of the error; additionally it generates information about the
direction into which some element has to be refined to reduce the
error in a proper way. Numerical examples are presented for 2-d rectangular
and 3-d prismatic grids.
%0 Journal Article
%1 siebert1996posteriori
%A Siebert, Kunibert G.
%D 1996
%K fis ians liste
%N 3
%P 373-398
%R 10.1007/s002110050197
%T An a posteriori error estimator for anisotropic refinement
%V 73
%X Besides an algorithm for local refinement, an a posteriori error estimator
is the basic tool of every adaptive finite element method. Using
information generated by such an error estimator the refinement of
the grid is controlled. For 2nd order elliptic problems we present
an error estimator for anisotropically refined grids, like n -d cuboidal
and 3-d prismatic grids, that gives correct information about the
size of the error; additionally it generates information about the
direction into which some element has to be refined to reduce the
error in a proper way. Numerical examples are presented for 2-d rectangular
and 3-d prismatic grids.
@article{siebert1996posteriori,
abstract = {Besides an algorithm for local refinement, an a posteriori error estimator
is the basic tool of every adaptive finite element method. Using
information generated by such an error estimator the refinement of
the grid is controlled. For 2nd order elliptic problems we present
an error estimator for anisotropically refined grids, like n -d cuboidal
and 3-d prismatic grids, that gives correct information about the
size of the error; additionally it generates information about the
direction into which some element has to be refined to reduce the
error in a proper way. Numerical examples are presented for 2-d rectangular
and 3-d prismatic grids.},
added-at = {2019-06-17T14:25:24.000+0200},
author = {Siebert, Kunibert G.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2040e636ccd38d6fd2454d552d9fcbb62/britsteiner},
doi = {10.1007/s002110050197},
interhash = {7f352a7603963d7d74ac7b721bdb82c5},
intrahash = {040e636ccd38d6fd2454d552d9fcbb62},
issn = {{0029-599X} and {0945-3245}},
journaltitle = {Numerische Mathematik},
keywords = {fis ians liste},
language = {eng},
number = 3,
pages = {373-398},
timestamp = {2019-06-17T12:34:15.000+0200},
title = {An a posteriori error estimator for anisotropic refinement},
volume = 73,
year = 1996
}