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Robustness of finite element simulations in densely packed random particle composites
1. | Humboldt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany |
References:
[1] |
I. Babuška and B. Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data. II: The trace spaces and application to the boundary value problems with nonhomogeneous boundary conditions,, SIAM J. Math. Anal., 20 (1989), 763.
doi: 10.1137/0520054. |
[2] |
L. Berlyand and A. Kolpakov, Network approximation in the limit of small interparticle distance of the effective properties of a high-contrast random dispersed composite,, Arch. Ration. Mech. Anal., 159 (2001), 179.
doi: 10.1007/s002050100142. |
[3] |
L. Berlyand and A. Novikov, Error of the network approximation for densely packed composites with irregular geometry,, SIAM J. Math. Anal., 34 (2002), 385.
doi: 10.1137/S0036141001397144. |
[4] |
L. Borcea and G. C. Papanicolaou, Network approximation for transport properties of high contrast materials,, SIAM J. Appl. Math., 58 (1998), 501.
doi: 10.1137/S0036139996301891. |
[5] |
G. A. Chechkin, Yu. O. Koroleva and L.-E. Persson, On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure,, J. Inequal. Appl., 2007 (3413).
|
[6] |
L. C. Evans, "Partial Differential Equations,'' 2nd edition,, Graduate Studies in Mathematics, 19 (2010).
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[7] |
J. M. Melenk, "$hp$-Finite Element Methods for Singular Perturbations,'', Lecture Notes in Mathematics, 1796 (2002).
|
[8] |
D. Peterseim, Generalized delaunay partitions and composite material modeling, preprint,, DFG Research Center Matheon Berlin, 690 (2010). Google Scholar |
[9] |
D. Peterseim, Triangulating a system of disks,, in, (2010), 241. Google Scholar |
[10] |
D. Peterseim and C. Carstensen, Finite element network approximation of conductivity in particle composites,, preprint, 807 (2010). Google Scholar |
show all references
References:
[1] |
I. Babuška and B. Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data. II: The trace spaces and application to the boundary value problems with nonhomogeneous boundary conditions,, SIAM J. Math. Anal., 20 (1989), 763.
doi: 10.1137/0520054. |
[2] |
L. Berlyand and A. Kolpakov, Network approximation in the limit of small interparticle distance of the effective properties of a high-contrast random dispersed composite,, Arch. Ration. Mech. Anal., 159 (2001), 179.
doi: 10.1007/s002050100142. |
[3] |
L. Berlyand and A. Novikov, Error of the network approximation for densely packed composites with irregular geometry,, SIAM J. Math. Anal., 34 (2002), 385.
doi: 10.1137/S0036141001397144. |
[4] |
L. Borcea and G. C. Papanicolaou, Network approximation for transport properties of high contrast materials,, SIAM J. Appl. Math., 58 (1998), 501.
doi: 10.1137/S0036139996301891. |
[5] |
G. A. Chechkin, Yu. O. Koroleva and L.-E. Persson, On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure,, J. Inequal. Appl., 2007 (3413).
|
[6] |
L. C. Evans, "Partial Differential Equations,'' 2nd edition,, Graduate Studies in Mathematics, 19 (2010).
|
[7] |
J. M. Melenk, "$hp$-Finite Element Methods for Singular Perturbations,'', Lecture Notes in Mathematics, 1796 (2002).
|
[8] |
D. Peterseim, Generalized delaunay partitions and composite material modeling, preprint,, DFG Research Center Matheon Berlin, 690 (2010). Google Scholar |
[9] |
D. Peterseim, Triangulating a system of disks,, in, (2010), 241. Google Scholar |
[10] |
D. Peterseim and C. Carstensen, Finite element network approximation of conductivity in particle composites,, preprint, 807 (2010). Google Scholar |
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