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 Generic
%1 kreuzer2012design
%A Kreuzer, Christian
%A Möller, Christian
%A Schmidt, Alfred
%A Siebert, Kunibert G.
%D 2012
%J IMA Journal of Numerical Analysis
%K adaptive analysis convergence elements, finite parabolic problems, vorlaeufig
%R 10.1093/imanum/drr026
%T Design and Convergence Analysis for an Adaptive Discretization of
the Heat Equation
%U http://dx.doi.org/10.1093/imanum/drr026
%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).
@electronic{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 = {2018-07-20T10:54:15.000+0200},
author = {Kreuzer, Christian and M\"oller, Christian and Schmidt, Alfred and Siebert, Kunibert G.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21237a0ffaf182fdd91641c941d3d4db1/mhartmann},
doi = {10.1093/imanum/drr026},
howpublished = {IMA J. Numer. Anal. doi:10.1093/imanum/drr026},
interhash = {4f9e70559b93e67305a10572434e4d6a},
intrahash = {1237a0ffaf182fdd91641c941d3d4db1},
journal = {IMA Journal of Numerical Analysis},
keywords = {adaptive analysis convergence elements, finite parabolic problems, vorlaeufig},
note = {Online First},
owner = {kohlsk},
timestamp = {2018-07-20T08:54:15.000+0200},
title = {Design and Convergence Analysis for an Adaptive Discretization of
the Heat Equation},
url = {http://dx.doi.org/10.1093/imanum/drr026},
year = 2012
}