Mathematically Founded Design of Adaptive Finite Element Software
K. Siebert. Multiscale and Adaptivity : modeling, numerics and applications, 2040, page 227-309. Heidelberg, Springer, (2012)
DOI: 10.1007/978-3-642-24079-9_4
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.
%0 Conference Paper
%1 siebert2012mathematically
%A Siebert, Kunibert G.
%B Multiscale and Adaptivity : modeling, numerics and applications
%C Heidelberg
%D 2012
%E Naldi, Giovanni
%E Russo, Giovanni
%I Springer
%K liste ubs_10008 ubs_20013 ubs_30123 unibibliografie
%N 2040
%P 227-309
%R 10.1007/978-3-642-24079-9_4
%T Mathematically Founded Design of Adaptive Finite Element Software
%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 = {2020-03-27T16:33:18.000+0100},
address = {Heidelberg},
author = {Siebert, Kunibert G.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2a1a99d3099abf222e9d2d632c6fd7468/unibiblio},
booktitle = {Multiscale and Adaptivity : modeling, numerics and applications},
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 = {a1a99d3099abf222e9d2d632c6fd7468},
keywords = {liste ubs_10008 ubs_20013 ubs_30123 unibibliografie},
language = {eng},
number = 2040,
pages = {227-309},
publisher = {Springer},
series = {Lecture notes in mathematics},
timestamp = {2020-03-27T15:33:18.000+0100},
title = {Mathematically Founded Design of Adaptive Finite Element Software},
venue = {Cetraro},
year = 2012
}