-
2
-
-
21144473666
-
Homogenization and two-scale convergence
-
MR1185639 (93k:35022)
-
G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23(1992), 1482-1518. MR1185639 (93k:35022)
-
(1992)
SIAM J. Math. Anal.
, vol.23
, pp. 1482-1518
-
-
Allaire, G.1
-
3
-
-
0017266319
-
Homogenization and its applications, mathematical and computational problems
-
(SYNSPADE 1975, College Park, MD, May 1975) (B. Hubbard ed.), Academic Press, New York. MR0502025 (58:19215)
-
I. Babuska, Homogenization and its applications, mathematical and computational problems, Numerical Solutions of Partial Differential Equations-III (SYNSPADE 1975, College Park, MD, May 1975) (B. Hubbard ed.), Academic Press, New York, 1976, pp. 89-116. MR0502025 (58:19215)
-
(1976)
Numerical Solutions of Partial Differential Equations-III
, pp. 89-116
-
-
Babuska, I.1
-
4
-
-
0001485798
-
Solution of interface by homogenization. I, II, III
-
MR0509273 (58:23013a); MR0509277 (58:23013b); MR0509282 (58:23014)
-
I. Babuska, Solution of interface by homogenization. I, II, III, SIAM J. Math. Anal., 7 (1976), 603-634, 635-645, 8 (1977), 923-937. MR0509273 (58:23013a); MR0509277 (58:23013b); MR0509282 (58:23014)
-
(1976)
SIAM J. Math. Anal.
, vol.7-8
, pp. 603-634
-
-
Babuska, I.1
-
6
-
-
0005722058
-
Homogénéisation de problémes quasi-linéaires
-
L. Boccardo and F. Murat, Homogénéisation de problémes quasi-linéaires, Publ. IRMA, Lille., 3 (1981), no. 7, 13-51.
-
(1981)
Publ. IRMA, Lille.
, vol.3
, Issue.7
, pp. 13-51
-
-
Boccardo, L.1
Murat, F.2
-
7
-
-
0005225771
-
Numerical experiments of the homogenization method for operators with periodic coefficients
-
Springer-Verlag. MR0540121 (80e:65108)
-
J.F. Bourgat, Numerical experiments of the homogenization method for operators with periodic coefficients, Lecture Notes in Mathematics, Vol. 707. Springer-Verlag, 1977, pp. 330-356. MR0540121 (80e:65108)
-
(1977)
Lecture Notes in Mathematics
, vol.707
, pp. 330-356
-
-
Bourgat, J.F.1
-
8
-
-
84966233568
-
Multi-level adaptive solutions to boundary-value problems
-
MR0431719 (55:4714)
-
A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp., 31 (1977), 333-390. MR0431719 (55:4714)
-
(1977)
Math. Comp.
, vol.31
, pp. 333-390
-
-
Brandt, A.1
-
11
-
-
0002590226
-
The combined effect of curved boundaries and numerical integration in isoparametric finite element methods
-
(A. K. Aziz ed.), Academic Press, Inc., MR0421108 (54:9113)
-
P.G. Ciarlet and P.-A. Raviart, The combined effect of curved boundaries and numerical integration in isoparametric finite element methods, The Mathematics Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz ed.), Academic Press, Inc., 1972, pp. 409-474. MR0421108 (54:9113)
-
(1972)
The Mathematics Foundations of the Finite Element Method with Applications to Partial Differential Equations
, pp. 409-474
-
-
Ciarlet, P.G.1
Raviart, P.-A.2
-
12
-
-
0016541865
-
Approximation by finite element functions using local regularization
-
MR0400739 (53:4569)
-
P. Clément, Approximation by finite element functions using local regularization, RAIRO., 9 (1975), 77-84. MR0400739 (53:4569)
-
(1975)
RAIRO
, vol.9
, pp. 77-84
-
-
Clément, P.1
-
13
-
-
3042650414
-
On homogenization of elliptic equations with random coefficients
-
MR1768843 (2002j:35328)
-
J.G. Conlon and A. Naddaf, On homogenization of elliptic equations with random coefficients, Electron J. Probab., 5 (2000), 1-58. MR1768843 (2002j:35328)
-
(2000)
Electron J. Probab.
, vol.5
, pp. 1-58
-
-
Conlon, J.G.1
Naddaf, A.2
-
14
-
-
84944838250
-
Numerical calculation of equivalent grid block permeability tensors for heterogeneous poros-media
-
L.J. Durlofsky, Numerical calculation of equivalent grid block permeability tensors for heterogeneous poros-media, Water. Resour. Res., 28 (1992), 699-708.
-
(1992)
Water. Resour. Res.
, vol.28
, pp. 699-708
-
-
Durlofsky, L.J.1
-
15
-
-
84990622690
-
Homogenization of linear and nonlinear transport equations
-
MR1151269 (92k:35026)
-
W. E, Homogenization of linear and nonlinear transport equations, Comm. Pure Appl. Math., 45 (1992), 301-326. MR1151269 (92k:35026)
-
(1992)
Comm. Pure Appl. Math.
, vol.45
, pp. 301-326
-
-
E, W.1
-
16
-
-
85128805678
-
The heterogeneous multiscale methods
-
MR1979846 (2004b:35019)
-
W. E and B. Engquist, The heterogeneous multiscale methods, Comm. Math. Sci., 1(2003), 87-132. MR1979846 (2004b:35019)
-
(2003)
Comm. Math. Sci.
, vol.1
, pp. 87-132
-
-
E, W.1
Engquist, B.2
-
18
-
-
7244239706
-
Multiscale modeling and computation
-
MR2002752
-
W. E and B. Engquist, Multiscale modeling and computation, Notice Amer. Math. Soc., 50 (2003), 1062-1070. MR2002752
-
(2003)
Notice Amer. Math. Soc.
, vol.50
, pp. 1062-1070
-
-
E, W.1
Engquist, B.2
-
19
-
-
13644264576
-
Heterogeneous multiscale method for locally self-similar problems
-
W. E and X.Y. Yue, Heterogeneous multiscale method for locally self-similar problems, Comm. Math. Sci., 2 (2004), 137-144.
-
(2004)
Comm. Math. Sci.
, vol.2
, pp. 137-144
-
-
E, W.1
Yue, X.Y.2
-
20
-
-
0000713961
-
Convergence of a nonconforming multiscale finite element method
-
MR1740386 (2002a:65176)
-
Y.R. Efendiev, T. Hou and X. Wu, Convergence of a nonconforming multiscale finite element method, SIAM J. Numer. Anal., 37 (2000), 888-910. MR1740386 (2002a:65176)
-
(2000)
SIAM J. Numer. Anal.
, vol.37
, pp. 888-910
-
-
Efendiev, Y.R.1
Hou, T.2
Wu, X.3
-
23
-
-
0003002361
-
On the homogenization of guasilinear divergence structure operators
-
MR0916685 (89a:35025)
-
N. Fusco and G. Moscarielio, On the homogenization of guasilinear divergence structure operators, Ann. Mat. Pura. Appl., 146 (1987), 1-13. MR0916685 (89a:35025)
-
(1987)
Ann. Mat. Pura. Appl.
, vol.146
, pp. 1-13
-
-
Fusco, N.1
Moscarielio, G.2
-
25
-
-
0031161210
-
A multiscale finite element method for elliptic problems in composite materials and porous media
-
MR1455261 (98e:73132)
-
T. Hou and X. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134 (1997), 169-189. MR1455261 (98e:73132)
-
(1997)
J. Comput. Phys.
, vol.134
, pp. 169-189
-
-
Hou, T.1
Wu, X.2
-
26
-
-
85128858890
-
Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level analysis
-
MR2041455
-
I.G. Kevrekidis, C.W. Gear, J.M. Hyman, P.G. Kevrekidis, O. Runborg and C. Theodoropoulos, Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis, Comm, Math. Sci., 1 (2003), 715-762. MR2041455
-
(2003)
Comm, Math. Sci.
, vol.1
, pp. 715-762
-
-
Kevrekidis, I.G.1
Gear, C.W.2
Hyman, J.M.3
Kevrekidis, P.G.4
Runborg, O.5
Theodoropoulos, C.6
-
27
-
-
0035451516
-
An analysis of the quasicontinuum method
-
J. Knap and M. Ortiz, An analysis of the quasicontinuum method, J. Mech. Phys. Solids., 49 (2001), 1899-1923.
-
(2001)
J. Mech. Phys. Solids.
, vol.49
, pp. 1899-1923
-
-
Knap, J.1
Ortiz, M.2
-
28
-
-
0000254912
-
Homogenization of random operators
-
MR0542557 (81m:35142)
-
S.M. Kozlov, Homogenization of random operators, Math. USSR Sb., 37 (1980), 167-180. MR0542557 (81m:35142)
-
(1980)
Math. USSR Sb.
, vol.37
, pp. 167-180
-
-
Kozlov, S.M.1
-
29
-
-
0040788429
-
Generalized p-FEM in homogenization
-
MR1777492 (2001f:65139)
-
A.M. Matache, I. Babuska and C. Schwab, Generalized p-FEM in homogenization, Numer. Math., 88 (2000), 319-375. MR1777492 (2001f:65139)
-
(2000)
Numer. Math.
, vol.88
, pp. 319-375
-
-
Matache, A.M.1
Babuska, I.2
Schwab, C.3
-
30
-
-
0004025336
-
-
Cambridge University Press. MR1899805 (2003d:74077)
-
G.W. Milton, The Theory of Composites, Cambridge University Press, 2002. MR1899805 (2003d:74077)
-
(2002)
The Theory of Composites
-
-
Milton, G.W.1
-
32
-
-
33747491187
-
First order corrections to the homogenized eigenvalues of a periodic composite medium
-
MR1489436 (99g:35018)
-
S. Moskow and M. Vogelius, First order corrections to the homogenized eigenvalues of a periodic composite medium, Proc. Royal Soc. Edinburgh. Sec. A., 127 (1997), 1263-1299. MR1489436 (99g:35018)
-
(1997)
Proc. Royal Soc. Edinburgh. Sec. A.
, vol.127
, pp. 1263-1299
-
-
Moskow, S.1
Vogelius, M.2
-
33
-
-
13644266699
-
H-Convergence
-
F. Murat and L. Tartar, H-Convergence, Cours Peccot, 1977. Reprinted in Topics in the Mathematical Modeling of Composite Materials (A. Cherkaev and R. Kohn eds.), Birkhäuser, Boston, 1997, pp. 21-43. MR1493039
-
(1977)
Cours Peccot
-
-
Murat, F.1
Tartar, L.2
-
34
-
-
0003561270
-
-
Reprinted in Birkhäuser, Boston, MR1493039
-
F. Murat and L. Tartar, H-Convergence, Cours Peccot, 1977. Reprinted in Topics in the Mathematical Modeling of Composite Materials (A. Cherkaev and R. Kohn eds.), Birkhäuser, Boston, 1997, pp. 21-43. MR1493039
-
(1997)
Topics in the Mathematical Modeling of Composite Materials
, pp. 21-43
-
-
Cherkaev, A.1
Kohn, R.2
-
35
-
-
0000315621
-
A general convergence result for a functional related to the theory of homogenization
-
MR0990867 (90j:35030)
-
G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623. MR0990867 (90j:35030)
-
(1989)
SIAM J. Math. Anal.
, vol.20
, pp. 608-623
-
-
Nguetseng, G.1
-
36
-
-
0003071531
-
Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I. Error estimates and adaptive algorithms
-
MR1786241 (2001e:74079)
-
J.T. Oden and K.S. Vemaganti, Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I. Error estimates and adaptive algorithms, J. Comput. Phys., 164 (2000), 22-47. MR1786241 (2001e:74079)
-
(2000)
J. Comput. Phys.
, vol.164
, pp. 22-47
-
-
Oden, J.T.1
Vemaganti, K.S.2
-
37
-
-
0001689286
-
Boundary value problems with rapidly oscillating random coefficients
-
Esztergom, Hungary, 1979, published in Seria Colloquia Mathematica Societatis Janos Bolyai, North-Holland. MR0712714 (84k:58233)
-
G.C. Papanicolaou and S.R. S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, at Proceedings of the conference on Random Fields, Esztergom, Hungary, 1979, published in Seria Colloquia Mathematica Societatis Janos Bolyai, North-Holland, 27 (1981), pp. 835-873. MR0712714 (84k:58233)
-
(1981)
Proceedings of the Conference on Random Fields
, vol.27
, pp. 835-873
-
-
Papanicolaou, G.C.1
Varadhan, S.R.S.2
-
38
-
-
84968491183
-
Some optimal error estimates for piecewise linear finite element approximations
-
MR0645661 (83e:65180)
-
R. Rannacher and R. Scott, Some optimal error estimates for piecewise linear finite element approximations, Math. Comp., 38 (1982), 437-445. MR0645661 (83e:65180)
-
(1982)
Math. Comp.
, vol.38
, pp. 437-445
-
-
Rannacher, R.1
Scott, R.2
-
39
-
-
13644261985
-
Generalzied FEM for homogenization problems
-
Multiscale and Multiresolution Methods: Theory and Applications, (T. J. Earth, T. Chan and R. Heimes eds.), Springer-Verlag, Heidelberg. MR1928567 (20031:65115)
-
C. Schwab and A.-M. Matache, Generalzied FEM for homogenization problems, Multiscale and Multiresolution Methods: Theory and Applications, Lecture Notes in Computational Sciences and Engineering, Vol. 20 (T. J. Earth, T. Chan and R. Heimes eds.), Springer-Verlag, Heidelberg, 2002, pp. 197-237. MR1928567 (20031:65115)
-
(2002)
Lecture Notes in Computational Sciences and Engineering
, vol.20
, pp. 197-237
-
-
Schwab, C.1
Matache, A.-M.2
-
40
-
-
84966250424
-
∞ estimates for the finite element method on irregular meshes
-
MR0436617 (55:9560)
-
∞ estimates for the finite element method on irregular meshes, Math. Comp., 30 (1976), 681-697. MR0436617 (55:9560)
-
(1976)
Math. Comp.
, vol.30
, pp. 681-697
-
-
Scott, R.1
-
41
-
-
0017291333
-
Convergence in energy for elliptic operators
-
(SYNSPADE 1975, College Park, MD, May 1975) (B. Hubbard ed.), Academic Press, New York. MR0477444 (57:16971)
-
S. Spagnolo, Convergence in energy for elliptic operators, Numerical Solutions of Partial Differential Equations-III (SYNSPADE 1975, College Park, MD, May 1975) (B. Hubbard ed.), Academic Press, New York, 1976, pp. 469-499. MR0477444 (57:16971)
-
(1976)
Numerical Solutions of Partial Differential Equations-III
, pp. 469-499
-
-
Spagnolo, S.1
-
42
-
-
0010534121
-
An introduction to the homogenization method in optimal design
-
Optimal shape Design (A. Cellina and A. Ornelas eds.). Springer-verlag. MR1804685
-
L. Tartar, An introduction to the homogenization method in optimal design, Optimal shape Design (A. Cellina and A. Ornelas eds.), Lecture Notes in Mathematics, Vol. 1740. Springer-verlag, 2000. pp. 47-156. MR1804685
-
(2000)
Lecture Notes in Mathematics
, vol.1740
, pp. 47-156
-
-
Tartar, L.1
-
43
-
-
0001547745
-
Two-grid discretization techniques for linear and nonlinear PDE
-
MR1411848 (971:65169)
-
J. Xu, Two-grid discretization techniques for linear and nonlinear PDE, SIAM J. Numer. Anal., 33 (1996), 1759-1777. MR1411848 (971:65169)
-
(1996)
SIAM J. Numer. Anal.
, vol.33
, pp. 1759-1777
-
-
Xu, J.1
-
44
-
-
13644259712
-
Averaging of symmetric diffusion in random media
-
V.V. Yurinskii, Averaging of symmetric diffusion in random media, Sibirsk. Mat. Zh. 23 (1982), no. 2, 176-188; English transl, in Siberian Math J., 27 (1986), 603-613. MR0867870 (88e:35190)
-
(1982)
Sibirsk. Mat. Zh.
, vol.23
, Issue.2
, pp. 176-188
-
-
Yurinskii, V.V.1
-
45
-
-
10644259628
-
-
English transl, MR0867870 (88e:35190)
-
V.V. Yurinskii, Averaging of symmetric diffusion in random media, Sibirsk. Mat. Zh. 23 (1982), no. 2, 176-188; English transl, in Siberian Math J., 27 (1986), 603-613. MR0867870 (88e:35190)
-
(1986)
Siberian Math J.
, vol.27
, pp. 603-613
-
-
-
46
-
-
0034341523
-
On an extension of the method of two-scale convergence and its application
-
MR1809928 (2001k:35026)
-
V.V. Zhikov, On an extension of the method of two-scale convergence and its application, Sbornik: Mathematics, 191 (2000), 973-1014. MR1809928 (2001k:35026)
-
(2000)
Sbornik: Mathematics
, vol.191
, pp. 973-1014
-
-
Zhikov, V.V.1
|