Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case

Paola F. Antonietti; Blanca Ayuso

doi:10.1051/m2an:2007006

Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an:2007006 ◽

2007 ◽

Vol 41 (1) ◽

pp. 21-54 ◽

Cited By ~ 47

Author(s):

Paola F. Antonietti ◽

Blanca Ayuso

Keyword(s):

Domain Decomposition ◽

Discontinuous Galerkin ◽

Elliptic Problems ◽

Galerkin Approximations

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Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems

Journal of Numerical Mathematics ◽

10.1515/jnum.2011.008 ◽

2011 ◽

Vol 19 (3) ◽

Cited By ~ 7

Author(s):

A. T. Barker ◽

S. C. Brenner ◽

L.-Y. Sung

Keyword(s):

Domain Decomposition ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Local Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin ◽

Overlapping Schwarz

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A Uniform Additive Schwarz Preconditioner for High-Order Discontinuous Galerkin Approximations of Elliptic Problems

Journal of Scientific Computing ◽

10.1007/s10915-016-0259-9 ◽

2016 ◽

Vol 70 (2) ◽

pp. 608-630 ◽

Cited By ~ 9

Author(s):

Paola F. Antonietti ◽

Marco Sarti ◽

Marco Verani ◽

Ludmil T. Zikatanov

Keyword(s):

Discontinuous Galerkin ◽

Elliptic Problems ◽

High Order ◽

Additive Schwarz ◽

Galerkin Approximations ◽

Schwarz Preconditioner

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Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients

Mathematics of Computation ◽

10.1090/s0025-5718-2013-02760-3 ◽

2013 ◽

Vol 83 (287) ◽

pp. 1083-1120 ◽

Cited By ~ 11

Author(s):

Blanca Ayuso de Dios ◽

Michael Holst ◽

Yunrong Zhu ◽

Ludmil Zikatanov

Keyword(s):

Discontinuous Galerkin ◽

Elliptic Problems ◽

Multilevel Preconditioners ◽

Galerkin Approximations

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An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drp023 ◽

2009 ◽

Vol 31 (1) ◽

pp. 281-298 ◽

Cited By ~ 28

Author(s):

E. H. Georgoulis ◽

P. Houston ◽

J. Virtanen

Keyword(s):

Discontinuous Galerkin ◽

Fourth Order ◽

Elliptic Problems ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Error Indicator ◽

Galerkin Approximations

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Class of Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems

Lecture Notes in Computational Science and Engineering - Domain Decomposition Methods in Science and Engineering XVII ◽

10.1007/978-3-540-75199-1_19 ◽

2008 ◽

pp. 185-192 ◽

Cited By ~ 1

Author(s):

Paola F. Antonietti ◽

Blanca Ayuso

Keyword(s):

Discontinuous Galerkin ◽

Elliptic Problems ◽

Galerkin Approximations

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Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients

10.21236/ada580829 ◽

2010 ◽

Cited By ~ 2

Author(s):

Blanca A. de Dios ◽

Michael Holst ◽

Yunrong Zhu ◽

Ludmil Zikatanov

Keyword(s):

Discontinuous Galerkin ◽

Elliptic Problems ◽

Multilevel Preconditioners ◽

Galerkin Approximations

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Nonoverlapping Domain Decomposition Preconditioners for Discontinuous Galerkin Approximations of Hamilton–Jacobi–Bellman Equations

Journal of Scientific Computing ◽

10.1007/s10915-017-0428-5 ◽

2017 ◽

Vol 74 (1) ◽

pp. 145-174 ◽

Cited By ~ 5

Author(s):

Iain Smears

Keyword(s):

Domain Decomposition ◽

Discontinuous Galerkin ◽

Nonoverlapping Domain ◽

Bellman Equations ◽

Galerkin Approximations ◽

Nonoverlapping Domain Decomposition ◽

Hamilton Jacobi Bellman

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Domain Decomposition Preconditioning for Discontinuous Galerkin Approximations of Convection-Diffusion Problems

Lecture Notes in Computational Science and Engineering - Domain Decomposition Methods in Science and Engineering XVIII ◽

10.1007/978-3-642-02677-5_28 ◽

2009 ◽

pp. 259-266 ◽

Cited By ~ 2

Author(s):

Paola F. Antonietti ◽

Endre Süli

Keyword(s):

Domain Decomposition ◽

Discontinuous Galerkin ◽

Convection Diffusion ◽

Galerkin Approximations ◽

Diffusion Problems

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An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems

Mathematics of Computation ◽

10.1090/s0025-5718-03-01484-4 ◽

2003 ◽

Vol 72 (243) ◽

pp. 1215-1239 ◽

Cited By ~ 37

Author(s):

Caroline Lasser ◽

Andrea Toselli

Keyword(s):

Domain Decomposition ◽

Discontinuous Galerkin ◽

Advection Diffusion ◽

Galerkin Approximations ◽

Overlapping Domain Decomposition ◽

Diffusion Problems

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Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems

Numerical Methods for Partial Differential Equations ◽

10.1002/num.20386 ◽

2009 ◽

Vol 25 (4) ◽

pp. 952-971 ◽

Cited By ~ 20

Author(s):

Raytcho Lazarov ◽

Sergey Repin ◽

Satyendra K. Tomar

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

A Posteriori Error Estimates ◽

Elliptic Problems ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Galerkin Approximations

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