Convergence of the Heterogeneous Multiscale Finite Element Method for Elliptic Problems with Nonsmooth Microstructures

Rui Du; Pingbing Ming

doi:10.1137/090780754

Convergence of the Heterogeneous Multiscale Finite Element Method for Elliptic Problems with Nonsmooth Microstructures

Multiscale Modeling and Simulation ◽

10.1137/090780754 ◽

2010 ◽

Vol 8 (5) ◽

pp. 1770-1783 ◽

Cited By ~ 5

Author(s):

Rui Du ◽

Pingbing Ming

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elliptic Problems ◽

Multiscale Finite Element Method ◽

Multiscale Finite Element ◽

Heterogeneous Multiscale ◽

Element Method

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The heterogeneous multiscale finite element method FE-HMM for the homogenization of linear elastic solids

PAMM ◽

10.1002/pamm.201610249 ◽

2016 ◽

Vol 16 (1) ◽

pp. 521-522 ◽

Cited By ~ 3

Author(s):

Bernhard Eidel ◽

Andreas Fischer

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elastic Solids ◽

Linear Elastic ◽

Multiscale Finite Element Method ◽

Multiscale Finite Element ◽

Heterogeneous Multiscale ◽

Element Method

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A Combined Finite Element and Multiscale Finite Element Method for the Multiscale Elliptic Problems

Multiscale Modeling and Simulation ◽

10.1137/120898279 ◽

2014 ◽

Vol 12 (4) ◽

pp. 1424-1457 ◽

Cited By ~ 4

Author(s):

Weibing Deng ◽

Haijun Wu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elliptic Problems ◽

Multiscale Finite Element Method ◽

Multiscale Finite Element ◽

Element Method

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The heterogeneous multiscale finite element method for the homogenization of linear elastic solids and a comparison with the FE2 method

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2017.10.001 ◽

2018 ◽

Vol 329 ◽

pp. 332-368 ◽

Cited By ~ 10

Author(s):

Bernhard Eidel ◽

Andreas Fischer

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elastic Solids ◽

Linear Elastic ◽

Multiscale Finite Element Method ◽

Multiscale Finite Element ◽

Heterogeneous Multiscale ◽

Element Method

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Heterogeneous multiscale finite element method with novel numerical integration schemes

Communications in Mathematical Sciences ◽

10.4310/cms.2010.v8.n4.a4 ◽

2010 ◽

Vol 8 (4) ◽

pp. 863-885 ◽

Cited By ~ 12

Author(s):

Rui Du ◽

Pingbing Ming

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Integration ◽

Multiscale Finite Element Method ◽

Integration Schemes ◽

Multiscale Finite Element ◽

Heterogeneous Multiscale ◽

Element Method

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Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients

Mathematics of Computation ◽

10.1090/s0025-5718-99-01077-7 ◽

1999 ◽

Vol 68 (227) ◽

pp. 913-944 ◽

Cited By ~ 332

Author(s):

Thomas Y. Hou ◽

Xiao-Hui Wu ◽

Zhiqiang Cai

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elliptic Problems ◽

Multiscale Finite Element Method ◽

Oscillating Coefficients ◽

Multiscale Finite Element ◽

Element Method

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A multiscale finite element method for elliptic problems with highly oscillatory coefficients

Applied Numerical Mathematics ◽

10.1016/j.apnum.2003.12.002 ◽

2004 ◽

Vol 50 (1) ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Jinru Chen ◽

Junzhi Cui

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elliptic Problems ◽

Multiscale Finite Element Method ◽

Highly Oscillatory ◽

Multiscale Finite Element ◽

Element Method

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The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains

Numerische Mathematik ◽

10.1007/s00211-009-0244-4 ◽

2009 ◽

Vol 113 (4) ◽

pp. 601-629 ◽

Cited By ~ 42

Author(s):

Patrick Henning ◽

Mario Ohlberger

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Perforated Domains ◽

Multiscale Finite Element Method ◽

Multiscale Finite Element ◽

Heterogeneous Multiscale ◽

Homogenization Problems ◽

Element Method

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Computation of effective resistivity in materials with microinclusions by a heterogeneous multiscale finite element method

Physical Mesomechanics ◽

10.1134/s1029959917040051 ◽

2017 ◽

Vol 20 (4) ◽

pp. 407-416

Author(s):

M. I. Epov ◽

E. P. Shurina ◽

A. Yu. Kutischeva

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Multiscale Finite Element Method ◽

Effective Resistivity ◽

Multiscale Finite Element ◽

Heterogeneous Multiscale ◽

Element Method

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A mixed multiscale finite element method for elliptic problems with oscillating coefficients

Mathematics of Computation ◽

10.1090/s0025-5718-02-01441-2 ◽

2002 ◽

Vol 72 (242) ◽

pp. 541-577 ◽

Cited By ~ 269

Author(s):

Zhiming Chen ◽

Thomas Y. Hou

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Elliptic Problems ◽

Multiscale Finite Element Method ◽

Oscillating Coefficients ◽

Multiscale Finite Element ◽

Element Method

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A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media

Journal of Computational Physics ◽

10.1006/jcph.1997.5682 ◽

1997 ◽

Vol 134 (1) ◽

pp. 169-189 ◽

Cited By ~ 991

Author(s):

Thomas Y. Hou ◽

Xiao-Hui Wu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Porous Media ◽

Composite Materials ◽

Elliptic Problems ◽

Multiscale Finite Element Method ◽

Multiscale Finite Element ◽

Element Method

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