We develop a preconditioner for systems arising from space-time finite element discretizations of parabolic equations. The preconditioner is based on a transformation of the coupled system into block diagonal form and an efficient solution strategy for the arising blocks. The suggested strategy makes use of an inexact factorization of the Schur complement of these blocks, for which uniform bounds on the condition number can be proven. The main computational effort of the preconditioner lies in solving implicit Euler-like problems, which allows for the usage of efficient standard solvers. Numerical experiments are performed to corroborate our theoretical findings.
Accepté le :
DOI : 10.1051/m2an/2016055
Keywords: Finite element method, time discretization, discontinuous Galerkin, preconditioning
Basting, Steffen 1 ; Bänsch, Eberhard 2
@article{M2AN_2017__51_4_1173_0,
author = {Basting, Steffen and B\"ansch, Eberhard},
title = {Preconditioners for the {Discontinuous} {Galerkin} time-stepping method of arbitrary order},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1173--1195},
year = {2017},
publisher = {EDP Sciences},
volume = {51},
number = {4},
doi = {10.1051/m2an/2016055},
mrnumber = {3702409},
zbl = {1375.65131},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2016055/}
}
TY - JOUR AU - Basting, Steffen AU - Bänsch, Eberhard TI - Preconditioners for the Discontinuous Galerkin time-stepping method of arbitrary order JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1173 EP - 1195 VL - 51 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2016055/ DO - 10.1051/m2an/2016055 LA - en ID - M2AN_2017__51_4_1173_0 ER -
%0 Journal Article %A Basting, Steffen %A Bänsch, Eberhard %T Preconditioners for the Discontinuous Galerkin time-stepping method of arbitrary order %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1173-1195 %V 51 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2016055/ %R 10.1051/m2an/2016055 %G en %F M2AN_2017__51_4_1173_0
Basting, Steffen; Bänsch, Eberhard. Preconditioners for the Discontinuous Galerkin time-stepping method of arbitrary order. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1173-1195. doi: 10.1051/m2an/2016055
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