Multiplicative Schwarz methods for discontinuous Galerkin approximations of elliptic problems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) no. 3, p. 443-469
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.
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {3},
     year = {2008},
     pages = {443-469},
     doi = {10.1051/m2an:2008012},
     zbl = {1146.65081},
     mrnumber = {2423794},
     language = {en},
     url = {http://http://www.numdam.org/item/M2AN_2008__42_3_443_0}
}
Antonietti, Paola F.; Ayuso, Blanca. Multiplicative Schwarz methods for discontinuous Galerkin approximations of elliptic problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) no. 3, pp. 443-469. doi : 10.1051/m2an:2008012. http://www.numdam.org/item/M2AN_2008__42_3_443_0/

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