Overlapping Schwarz Preconditioner for Fourth Order Multiscale Elliptic Problems

Parallel Processing and Applied Mathematics - Lecture Notes in Computer Science ◽

10.1007/978-3-030-43222-5_21 ◽

2020 ◽

pp. 245-255

Author(s):

Leszek Marcinkowski ◽

Talal Rahman

Keyword(s):

Fourth Order ◽

Elliptic Problems ◽

Schwarz Preconditioner ◽

Overlapping Schwarz

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Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/s0045-7825(02)00286-4 ◽

2002 ◽

Vol 191 (34) ◽

pp. 3669-3750 ◽

Author(s):

G. Engel ◽

K. Garikipati ◽

T.J.R. Hughes ◽

M.G. Larson ◽

L. Mazzei ◽

...

Keyword(s):

Finite Element ◽

Continuum Mechanics ◽

Fourth Order ◽

Strain Gradient ◽

Elliptic Problems ◽

Gradient Elasticity ◽

Strain Gradient Elasticity ◽

Finite Element Approximations ◽

Discontinuous Finite Element ◽

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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) ◽

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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Additive Schwarz preconditioner for the finite volume element discretization of symmetric elliptic problems

BIT Numerical Mathematics ◽

10.1007/s10543-015-0581-x ◽

2015 ◽

Vol 56 (3) ◽

pp. 967-993 ◽

Author(s):

L. Marcinkowski ◽

T. Rahman ◽

A. Loneland ◽

J. Valdman

Keyword(s):

Finite Volume ◽

Elliptic Problems ◽

Volume Element ◽

Element Discretization ◽

Additive Schwarz ◽

Finite Volume Element ◽

Schwarz Preconditioner

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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 ◽

Author(s):

Paola F. Antonietti ◽

Marco Sarti ◽

Marco Verani ◽

Ludmil T. Zikatanov

Keyword(s):

Discontinuous Galerkin ◽

Elliptic Problems ◽

Additive Schwarz ◽

Galerkin Approximations ◽

Schwarz Preconditioner

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Comparison principles for some fourth order elliptic problems

Ordinary and Partial Differential Equations - Lecture Notes in Mathematics ◽

10.1007/bfb0065004 ◽

1982 ◽

pp. 272-279 ◽

Author(s):

Vinod B Goyal ◽

Philip W Schaefer

Keyword(s):

Fourth Order ◽

Elliptic Problems ◽

Comparison Principles

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Parallel multiplicative Schwarz preconditioner for solving nonselfadjoint elliptic problems

International Journal of Computer Mathematics ◽

10.1080/00207160.2020.1822995 ◽

2020 ◽

pp. 1-19

Author(s):

Ruyi Zhang ◽

Shishun Li

Keyword(s):

Elliptic Problems ◽

Schwarz Preconditioner

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Applying the FROSch Overlapping Schwarz Preconditioner to Dislocation Mechanics in Deal.II

PAMM ◽

10.1002/pamm.201900337 ◽

2019 ◽

Vol 19 (1) ◽

Author(s):

Alexander Heinlein ◽

Oliver Rheinbach ◽

Friederike Röver ◽

Stefan Sandfeld ◽

Dominik Steinberger

Keyword(s):

Dislocation Mechanics ◽

Schwarz Preconditioner ◽

Overlapping Schwarz

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AC0-weak Galerkin finite element method for fourth-order elliptic problems

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22050 ◽

2016 ◽

Vol 32 (3) ◽

pp. 1090-1104 ◽

Author(s):

Gang Chen ◽

Minfu Feng

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Fourth Order ◽

Elliptic Problems ◽

Galerkin Finite Element Method ◽

Weak Galerkin ◽

Galerkin Finite Element ◽

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Some fourth order nonlinear elliptic problems related to epitaxial growth

Journal of Differential Equations ◽

10.1016/j.jde.2012.12.012 ◽

2013 ◽

Vol 254 (6) ◽

pp. 2515-2531 ◽

Author(s):

Carlos Escudero ◽

Ireneo Peral

Keyword(s):

Epitaxial Growth ◽

Fourth Order ◽

Elliptic Problems ◽

Nonlinear Elliptic Problems ◽

Nonlinear Elliptic

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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 ◽

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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