We derive an algorithm for the adaptive approximation of solutions
to parabolic equations. It is based on adaptive finite elements in
space and the implicit Euler discretization in time with adaptive
time-step sizes. We prove that, given a positive tolerance for the
error, the adaptive algorithm reaches the final time with a space–time
error between continuous and discrete solution that is below the
given tolerance. Numerical experiments reveal a more than competitive
performance of our algorithm ASTFEM (adaptive space–time finite element
method).
%0 Journal Article
%1 kreuzer2012design
%A Kreuzer, Christian
%A Möller, Christian A.
%A Schmidt, Alfred
%A Siebert, Kunibert G.
%D 2012
%K ians liste unibibliografie
%N 4
%P 1375–1403
%R 10.1093/imanum/drr026
%T Design and Convergence Analysis for an Adaptive Discretization of the Heat Equation
%V 32
%X We derive an algorithm for the adaptive approximation of solutions
to parabolic equations. It is based on adaptive finite elements in
space and the implicit Euler discretization in time with adaptive
time-step sizes. We prove that, given a positive tolerance for the
error, the adaptive algorithm reaches the final time with a space–time
error between continuous and discrete solution that is below the
given tolerance. Numerical experiments reveal a more than competitive
performance of our algorithm ASTFEM (adaptive space–time finite element
method).
@article{kreuzer2012design,
abstract = {We derive an algorithm for the adaptive approximation of solutions
to parabolic equations. It is based on adaptive finite elements in
space and the implicit Euler discretization in time with adaptive
time-step sizes. We prove that, given a positive tolerance for the
error, the adaptive algorithm reaches the final time with a space–time
error between continuous and discrete solution that is below the
given tolerance. Numerical experiments reveal a more than competitive
performance of our algorithm ASTFEM (adaptive space–time finite element
method).},
added-at = {2019-06-17T14:25:24.000+0200},
author = {Kreuzer, Christian and Möller, Christian A. and Schmidt, Alfred and Siebert, Kunibert G.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/28fca239740919a2edba747a2be1915f8/britsteiner},
doi = {10.1093/imanum/drr026},
interhash = {8cb8952ea05b1a7da9074f13decd9459},
intrahash = {8fca239740919a2edba747a2be1915f8},
journalsubtitle = {IMAJNA},
journaltitle = {IMA journal of numerical analysis},
keywords = {ians liste unibibliografie},
language = {eng},
number = 4,
pages = {1375–1403},
timestamp = {2019-06-17T12:34:15.000+0200},
title = {Design and Convergence Analysis for an Adaptive Discretization of the Heat Equation},
volume = 32,
year = 2012
}