Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems

Paola F. Antonietti; Blanca Ayuso

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 3, page 443-469
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Antonietti, Paola F., and Ayuso, Blanca. "Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems." ESAIM: Mathematical Modelling and Numerical Analysis 42.3 (2008): 443-469. <http://eudml.org/doc/250353>.

@article{Antonietti2008,
abstract = { 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. },
author = {Antonietti, Paola F., Ayuso, Blanca},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Domain decomposition methods; Schwarz preconditioners; discontinuous Galerkin methods.; domain decomposition methods; discontinuous Galerkin method; elliptic boundary-value problems; Krylov space solvers},
language = {eng},
month = {4},
number = {3},
pages = {443-469},
publisher = {EDP Sciences},
title = {Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems},
url = {http://eudml.org/doc/250353},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Antonietti, Paola F.
AU - Ayuso, Blanca
TI - Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/4//
PB - EDP Sciences
VL - 42
IS - 3
SP - 443
EP - 469
AB - 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.
LA - eng
KW - Domain decomposition methods; Schwarz preconditioners; discontinuous Galerkin methods.; domain decomposition methods; discontinuous Galerkin method; elliptic boundary-value problems; Krylov space solvers
UR - http://eudml.org/doc/250353
ER -

References

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