Mathematically Founded Design of Adaptive Finite Element Software
K. Siebert. Multiscale and Adaptivity, Volume 2040 von Lecture notes in mathematics, Seite 227-309. Springer, (2012)
DOI: 10.1007/978-3-642-24079-9_4
Zusammenfassung
In these lecture notes we derive from the mathematical concepts of
adaptive finite element methods basic design principles of adaptive
finite element software. We introduce finite element spaces, discuss
local refinement of simplical grids, the assemblage and structure
of the discrete linear system, the computation of the error estimator,
and common adaptive strategies. The mathematical discussion naturally
leads to appropriate data structures and efficient algorithms for
the implementation. The theoretical part is complemented by exercises
giving an introduction to the implementation of solvers for linear
and nonlinear problems in the adaptive finite element toolbox ALBERTA.
%0 Conference Paper
%1 siebert2012mathematically
%A Siebert, Kunibert G.
%B Multiscale and Adaptivity
%D 2012
%E Naldi, Giovanni
%E Russo, Giovanni
%I Springer
%K ians liste unibibliografie
%N 2040
%P 227-309
%R 10.1007/978-3-642-24079-9_4
%T Mathematically Founded Design of Adaptive Finite Element Software
%V 2040
%X In these lecture notes we derive from the mathematical concepts of
adaptive finite element methods basic design principles of adaptive
finite element software. We introduce finite element spaces, discuss
local refinement of simplical grids, the assemblage and structure
of the discrete linear system, the computation of the error estimator,
and common adaptive strategies. The mathematical discussion naturally
leads to appropriate data structures and efficient algorithms for
the implementation. The theoretical part is complemented by exercises
giving an introduction to the implementation of solvers for linear
and nonlinear problems in the adaptive finite element toolbox ALBERTA.
@inproceedings{siebert2012mathematically,
abstract = {In these lecture notes we derive from the mathematical concepts of
adaptive finite element methods basic design principles of adaptive
finite element software. We introduce finite element spaces, discuss
local refinement of simplical grids, the assemblage and structure
of the discrete linear system, the computation of the error estimator,
and common adaptive strategies. The mathematical discussion naturally
leads to appropriate data structures and efficient algorithms for
the implementation. The theoretical part is complemented by exercises
giving an introduction to the implementation of solvers for linear
and nonlinear problems in the adaptive finite element toolbox ALBERTA.},
added-at = {2019-06-17T14:25:24.000+0200},
author = {Siebert, Kunibert G.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2978bc304d96ab841b12e645650a4d73f/britsteiner},
booksubtitle = {modeling, numerics and applications ; C.I.M.E. Summer School, Cetraro, Italy 2009},
booktitle = {Multiscale and Adaptivity},
doi = {10.1007/978-3-642-24079-9_4},
editor = {Naldi, Giovanni and Russo, Giovanni},
eventdate = {2009-07-06/2009-07-11},
eventtitle = {CIME-EMS Summer School in Applied Mathematics on Multiscale and Adaptivity: Modeling, Numerics and Applications},
interhash = {c09dedeab1911b4be28b18348c168d8a},
intrahash = {978bc304d96ab841b12e645650a4d73f},
keywords = {ians liste unibibliografie},
language = {eng},
location = {Heidelberg},
number = 2040,
pages = {227-309},
publisher = {Springer},
series = {Lecture notes in mathematics},
timestamp = {2019-06-17T12:34:15.000+0200},
title = {Mathematically Founded Design of Adaptive Finite Element Software},
venue = {Cetraro},
volume = 2040,
year = 2012
}