Two-Level Additive Schwarz Methods for a Discontinuous Galerkin Approximation of Second Order Elliptic Problems

Xiaobing Feng; Ohannes A. Karakashian

doi:10.1137/s0036142900378480

Two-Level Additive Schwarz Methods for a Discontinuous Galerkin Approximation of Second Order Elliptic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142900378480 ◽

2001 ◽

Vol 39 (4) ◽

pp. 1343-1365 ◽

Cited By ~ 67

Author(s):

Xiaobing Feng ◽

Ohannes A. Karakashian

Keyword(s):

Discontinuous Galerkin ◽

Galerkin Approximation ◽

Elliptic Problems ◽

Second Order ◽

Schwarz Methods ◽

Additive Schwarz ◽

Second Order Elliptic Problems ◽

Additive Schwarz Methods

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Two-level additive Schwarz methods for discontinuous Galerkin approximations of second-order elliptic problems

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drw061 ◽

2016 ◽

pp. drw061 ◽

Cited By ~ 1

Author(s):

Ohannes Karakashian ◽

Craig Collins

Keyword(s):

Discontinuous Galerkin ◽

Elliptic Problems ◽

Second Order ◽

Schwarz Methods ◽

Additive Schwarz ◽

Galerkin Approximations ◽

Second Order Elliptic Problems ◽

Additive Schwarz Methods

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A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142902405217 ◽

2003 ◽

Vol 41 (6) ◽

pp. 2374-2399 ◽

Cited By ~ 200

Author(s):

Ohannes A. Karakashian ◽

Frederic Pascal

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

A Posteriori Error Estimates ◽

Galerkin Approximation ◽

Elliptic Problems ◽

Posteriori Error ◽

Second Order ◽

A Posteriori ◽

A Posteriori Error ◽

Second Order Elliptic Problems

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Convergence and Superconvergence of the Local Discontinuous Galerkin Method for Semilinear Second-Order Elliptic Problems on Cartesian Grids

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-021-00123-8 ◽

2021 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Cartesian Grids ◽

Local Discontinuous Galerkin ◽

Convergence And Superconvergence ◽

Second Order Elliptic Problems

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Additive Schwarz Methods for DG Discretization of Elliptic Problems with Discontinuous Coefficient

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

10.1007/978-3-319-18827-0_15 ◽

2016 ◽

pp. 167-175 ◽

Cited By ~ 1

Author(s):

Maksymilian Dryja ◽

Piotr Krzyżanowski

Keyword(s):

Elliptic Problems ◽

Discontinuous Coefficient ◽

Schwarz Methods ◽

Additive Schwarz ◽

Additive Schwarz Methods

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Pointwise Error Estimates of Discontinuous Galerkin Methods with Penalty for Second-Order Elliptic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142903421527 ◽

2004 ◽

Vol 42 (3) ◽

pp. 1146-1166 ◽

Cited By ~ 35

Author(s):

Zhangxin Chen ◽

Hongsen Chen

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Problems ◽

Second Order ◽

Galerkin Methods ◽

Pointwise Error ◽

Pointwise Error Estimates ◽

Second Order Elliptic Problems

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A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2014.09.036 ◽

2015 ◽

Vol 292 ◽

pp. 243-256 ◽

Cited By ~ 18

Author(s):

Yalchin Efendiev ◽

Raytcho Lazarov ◽

Minam Moon ◽

Ke Shi

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Second Order ◽

Hybridizable Discontinuous Galerkin ◽

Hybridizable Discontinuous Galerkin Method ◽

Second Order Elliptic Problems

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Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/070706616 ◽

2009 ◽

Vol 47 (2) ◽

pp. 1319-1365 ◽

Cited By ~ 523

Author(s):

Bernardo Cockburn ◽

Jayadeep Gopalakrishnan ◽

Raytcho Lazarov

Keyword(s):

Discontinuous Galerkin ◽

Elliptic Problems ◽

Second Order ◽

Galerkin Methods ◽

Continuous Galerkin ◽

Continuous Galerkin Methods ◽

Second Order Elliptic Problems

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Tutorial on Hybridizable Discontinuous Galerkin (HDG) for Second-Order Elliptic Problems

Advanced Finite Element Technologies - CISM International Centre for Mechanical Sciences ◽

10.1007/978-3-319-31925-4_5 ◽

2016 ◽

pp. 105-129 ◽

Cited By ~ 12

Author(s):

Ruben Sevilla ◽

Antonio Huerta

Keyword(s):

Discontinuous Galerkin ◽

Elliptic Problems ◽

Second Order ◽

Hybridizable Discontinuous Galerkin ◽

Second Order Elliptic Problems

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Low Order Discontinuous Galerkin Methods for Second Order Elliptic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/070685105 ◽

2009 ◽

Vol 47 (1) ◽

pp. 508-533 ◽

Cited By ~ 11

Author(s):

E. Burman ◽

B. Stamm

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Problems ◽

Second Order ◽

Galerkin Methods ◽

Second Order Elliptic Problems ◽

Low Order

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Two-Level Schwarz Methods for a Discontinuous Galerkin Approximation of Elliptic Problems with Jump Coefficients

Journal of Scientific Computing ◽

10.1007/s10915-020-01257-2 ◽

2020 ◽

Vol 84 (1) ◽

Author(s):

Yingzhi Liu ◽

Yinnian He

Keyword(s):

Discontinuous Galerkin ◽

Galerkin Approximation ◽

Elliptic Problems ◽

Schwarz Methods

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