In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, and we show that the resulting methods can be accelerated by using suitable Krylov space solvers. A discussion on the issue of preconditioning non-symmetric DG approximations of elliptic problems is also included. Extensive numerical experiments to confirm the theoretical results and to assess the robustness and the efficiency of the proposed preconditioners are provided.
Mots-clés : domain decomposition methods, Schwarz preconditioners, discontinuous Galerkin methods
@article{M2AN_2008__42_3_443_0,
author = {Antonietti, Paola F. and Ayuso, Blanca},
title = {Multiplicative {Schwarz} methods for discontinuous {Galerkin} approximations of elliptic problems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {443--469},
publisher = {EDP-Sciences},
volume = {42},
number = {3},
year = {2008},
doi = {10.1051/m2an:2008012},
mrnumber = {2423794},
zbl = {1146.65081},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2008012/}
}
TY - JOUR AU - Antonietti, Paola F. AU - Ayuso, Blanca TI - Multiplicative Schwarz methods for discontinuous Galerkin approximations of elliptic problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 443 EP - 469 VL - 42 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008012/ DO - 10.1051/m2an:2008012 LA - en ID - M2AN_2008__42_3_443_0 ER -
%0 Journal Article %A Antonietti, Paola F. %A Ayuso, Blanca %T Multiplicative Schwarz methods for discontinuous Galerkin approximations of elliptic problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 443-469 %V 42 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008012/ %R 10.1051/m2an:2008012 %G en %F M2AN_2008__42_3_443_0
Antonietti, Paola F.; Ayuso, Blanca. Multiplicative Schwarz methods for discontinuous Galerkin approximations of elliptic problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 443-469. doi : 10.1051/m2an:2008012. http://www.numdam.org/articles/10.1051/m2an:2008012/
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