Mathematically Founded Design of Adaptive Finite Element Software
K. Siebert. Multiscale and Adaptivity: Modelling, Numerics and Applications, volume 2040 of Lecture Notes in Math., Springer, Berlin, (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 Book Section
%1 siebert2012mathematically
%A Siebert, Kunibert G.
%B Multiscale and Adaptivity: Modelling, Numerics and Applications
%C Berlin
%D 2012
%I Springer
%K from:mhartmann ians imported vorlaeufig
%P 227-309
%R 10.1007/978-3-642-24079-9_4
%T Mathematically Founded Design of Adaptive Finite Element Software
%U http://dx.doi.org/10.1007/978-3-642-24079-9_4
%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.
@incollection{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 = {2018-07-20T10:54:49.000+0200},
address = {Berlin},
author = {Siebert, Kunibert G.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2a30be8489be43948971cf957b07e4adb/mathematik},
booktitle = {Multiscale and Adaptivity: Modelling, Numerics and Applications},
doi = {10.1007/978-3-642-24079-9_4},
interhash = {c09dedeab1911b4be28b18348c168d8a},
intrahash = {a30be8489be43948971cf957b07e4adb},
keywords = {from:mhartmann ians imported vorlaeufig},
owner = {kohlsk},
pages = {227-309},
publisher = {Springer},
series = {Lecture Notes in Math.},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {Mathematically Founded Design of Adaptive Finite Element Software},
url = {http://dx.doi.org/10.1007/978-3-642-24079-9_4},
volume = 2040,
year = 2012
}