Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations

Zhiqiang Cai; Xiu Ye; Shun Zhang

doi:10.1137/100805133

Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations

SIAM Journal on Numerical Analysis ◽

10.1137/100805133 ◽

2011 ◽

Vol 49 (5) ◽

pp. 1761-1787 ◽

Cited By ~ 56

Author(s):

Zhiqiang Cai ◽

Xiu Ye ◽

Shun Zhang

Keyword(s):

Finite Element ◽

A Priori ◽

Posteriori Error ◽

Interface Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Discontinuous Galerkin Finite Element ◽

Galerkin Finite Element Methods ◽

Error Estimations

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A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations

IMA Journal of Numerical Analysis ◽

10.1093/imanum/dry003 ◽

2018 ◽

Author(s):

Carsten Carstensen ◽

Gouranga Mallik ◽

Neela Nataraj

Keyword(s):

Finite Element ◽

Discontinuous Galerkin ◽

Error Control ◽

A Priori ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Discontinuous Galerkin Finite Element ◽

Galerkin Finite Element Methods

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A posteriori error analysis of hp-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drm009 ◽

2007 ◽

Vol 28 (2) ◽

pp. 245-273 ◽

Cited By ~ 33

Author(s):

P. Houston ◽

E. Suli ◽

T. P. Wihler

Keyword(s):

Finite Element ◽

Posteriori Error ◽

Elliptic Pdes ◽

A Posteriori ◽

A Posteriori Error Analysis ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Discontinuous Galerkin Finite Element ◽

Galerkin Finite Element Methods ◽

Posteriori Error Analysis

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A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods

Recent Advances in Adaptive Computation - Contemporary Mathematics ◽

10.1090/conm/383/07154 ◽

2005 ◽

pp. 1-14 ◽

Cited By ~ 13

Author(s):

Mark Ainsworth

Keyword(s):

Finite Element ◽

Discontinuous Galerkin ◽

Error Estimation ◽

Posteriori Error ◽

A Posteriori ◽

Posteriori Error Estimation ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Discontinuous Galerkin Finite Element ◽

Galerkin Finite Element Methods

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A priori and a posteriori error analysis for the mixed discontinuous Galerkin finite element approximations of the biharmonic problems

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22090 ◽

2016 ◽

Vol 33 (1) ◽

pp. 318-353 ◽

Cited By ~ 1

Author(s):

Chunguang Xiong ◽

Roland Becker ◽

Fusheng Luo ◽

Xiuling Ma

Keyword(s):

A Priori ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error Analysis ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Finite Element Approximations ◽

Discontinuous Galerkin Finite Element ◽

Posteriori Error Analysis ◽

Biharmonic Problems

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A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

Journal of Scientific Computing ◽

10.1007/s10915-013-9771-3 ◽

2013 ◽

Vol 59 (2) ◽

pp. 496-511 ◽

Cited By ~ 32

Author(s):

Long Chen ◽

Junping Wang ◽

Xiu Ye

Keyword(s):

Finite Element ◽

Finite Element Methods ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

A Posteriori ◽

Weak Galerkin ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Galerkin Finite Element Methods ◽

Second Order Elliptic Problems

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Fully Computable a Posteriori Error Bounds for Hybridizable Discontinuous Galerkin Finite Element Approximations

Journal of Scientific Computing ◽

10.1007/s10915-018-0715-9 ◽

2018 ◽

Vol 77 (1) ◽

pp. 443-466 ◽

Cited By ~ 6

Author(s):

Mark Ainsworth ◽

Guosheng Fu

Keyword(s):

Finite Element ◽

Error Bounds ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Finite Element Approximations ◽

Hybridizable Discontinuous Galerkin ◽

Discontinuous Galerkin Finite Element ◽

A Posteriori Error Bounds

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A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation

SIAM Journal on Numerical Analysis ◽

10.1137/060665993 ◽

2007 ◽

Vol 45 (4) ◽

pp. 1777-1798 ◽

Cited By ~ 72

Author(s):

Mark Ainsworth

Keyword(s):

Finite Element ◽

Error Estimation ◽

Finite Element Approximation ◽

Posteriori Error ◽

Element Approximation ◽

A Posteriori ◽

Posteriori Error Estimation ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Discontinuous Galerkin Finite Element

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A priori and a posteriori error analysis for discontinuous Galerkin finite element approximations of biharmonic eigenvalue problems

Advances in Computational Mathematics ◽

10.1007/s10444-019-09689-7 ◽

2019 ◽

Vol 45 (5-6) ◽

pp. 2623-2646 ◽

Cited By ~ 3

Author(s):

Liang Wang ◽

Chunguang Xiong ◽

Huibin Wu ◽

Fusheng Luo

Keyword(s):

Eigenvalue Problems ◽

A Priori ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Finite Element Approximations ◽

Discontinuous Galerkin Finite Element ◽

Posteriori Error Analysis ◽

Biharmonic Eigenvalue Problems

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Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates

SIAM Journal on Numerical Analysis ◽

10.1137/16m1056171 ◽

2017 ◽

Vol 55 (1) ◽

pp. 400-418 ◽

Cited By ~ 16

Author(s):

Zhiqiang Cai ◽

Cuiyu He ◽

Shun Zhang

Keyword(s):

Finite Element ◽

Error Estimates ◽

Finite Element Methods ◽

A Priori ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Interface Problems ◽

A Posteriori ◽

A Posteriori Error ◽

Discontinuous Finite Element

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A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes

Communications in Computational Physics ◽

10.4208/cicp.oa-2018-0058 ◽

2019 ◽

Vol 26 (2) ◽

pp. 558-578 ◽

Cited By ~ 2

Author(s):

Hengguang Li

Keyword(s):

Finite Element ◽

Finite Element Methods ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

A Posteriori ◽

Weak Galerkin ◽

A Posteriori Error ◽

Galerkin Finite Element ◽

Galerkin Finite Element Methods ◽

Polytopal Meshes

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