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All issues Volume 56 / No 4 (July-August 2022) ESAIM: M2AN, 56 4 (2022) 1451-1481 References
Open Access
Issue
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
Page(s) 1451 - 1481
DOI https://doi.org/10.1051/m2an/2022046
Published online 13 July 2022
  1. A. Abdulle, E. Weinan, B. Engquist and E. Vanden-Eijnden, The heterogeneous multiscale method. Acta Numer. 21 (2012) 1–87. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [Google Scholar]
  3. G. Allaire and M. Briane, Multiscale convergence and reiterated homogenisation. Proc. R. Soc. Edinburgh Sect. A Math. 126 (1996) 297–342. [CrossRef] [Google Scholar]
  4. L. Baffico, C. Grandmont, Y. Maday and A. Osses, Homogenization of elastic media with gaseous inclusions. Multiscale Model. Simul. 7 (2008) 432–465. [CrossRef] [MathSciNet] [Google Scholar]
  5. R.E. Bank, A.H. Sherman and A. Weiser, Some refinement algorithms and data structures for regular local mesh refinement. Sci. Comput. App. Math. Comput. Phys. Sci. 1 (1983) 3–17. [Google Scholar]
  6. J. Bey, Simplicial grid refinement: on Freudenthal’s algorithm and the optimal number of congruence classes. Numer. Math. 85 (2000) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  7. S.C. Brenner, Two-level additive Schwarz preconditioners for nonconforming finite elements. Contemp. Math. 180 (1994) 9. [CrossRef] [Google Scholar]
  8. C. Carstensen, Clément interpolation and its role in adaptive finite element error control. In: Partial Differential Equations and Functional Analysis. Springer (2006) 27–43. [CrossRef] [Google Scholar]
  9. P. Cazeaux, C. Grandmont and Y. Maday, Homogenization of a model for the propagation of sound in the lungs. Multiscale Model. Simul. 13 (2015) 43–71. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. Cioranescu, A. Damlamian and J. Orlik, Homogenization via unfolding in periodic elasticity with contact on closed and open cracks. Asymptotic Anal. 82 (2013) 201–232. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Clément, Approximation by finite element functions using local regularization. Revue française d’automatique, informatique, recherche opérationnelle. Analyse numérique 9 (1975) 77–84. [Google Scholar]
  12. P. Donato and S. Monsurro, Homogenization of two heat conductors with an interfacial contact resistance. Anal. App. 2 (2004) 247–273. [CrossRef] [Google Scholar]
  13. Y. Efendiev and T.Y. Hou, Multiscale Finite Element Methods: Theory and Applications. Vol. 4. Springer Science & Business Media (2009). [Google Scholar]
  14. A. Ern and J.-L. Guermond, Finite element quasi-interpolation and best approximation. ESAIM: M2AN 51 (2017) 1367–1385. [EDP Sciences] [Google Scholar]
  15. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press (2015). [Google Scholar]
  16. X. Gao and K. Wang, Strength of stick-slip and creeping subduction megathrusts from heat flow observations. Science 345 (2014) 1038–1041. [Google Scholar]
  17. D.S. Grebenkov, M. Filoche and B. Sapoval, Mathematical basis for a general theory of Laplacian transport towards irregular interfaces. Phys. Rev. E 73 (2006) 021103. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  18. I. Gruais and D. Poliševski, Heat transfer models for two-component media with interfacial jump. Applicable Anal. 96 (2017) 247–260. [CrossRef] [MathSciNet] [Google Scholar]
  19. W. Hackbusch and S.A. Sauter, Composite finite elements for the approximation of pdes on domains with complicated micro-structures. Numer. Math. 75 (1997) 447–472. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Heida, Stochastic homogenization of heat transfer in polycrystals with nonlinear contact conductivities. Applicable Anal. 91 (2012) 1243–1264. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Heida, R. Kornhuber and J. Podlesny, Fractal homogenization of multiscale interface problems. Multiscale Model. Simul. 18 (2020) 294–314. [CrossRef] [MathSciNet] [Google Scholar]
  22. T.Y. Hou and X.-H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169–189. [Google Scholar]
  23. T.J.R. Hughes, G.R. Feijóo, L. Mazzei and J.B. Quincy, The variational multiscale method a paradigm for computational mechanics. Comput. Methods Appl. Mech. Eng. 166 (1998) 3–24. [CrossRef] [Google Scholar]
  24. H.K. Hummel, Homogenization of Periodic and Random Multidimensional Microstructures. Ph.D. thesis, Technische Universität Bergakademie Freiberg (1999). [Google Scholar]
  25. V.V. Jikov, S.M. Kozlov and O.A. Olenik, Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin (1994). [CrossRef] [Google Scholar]
  26. R. Kornhuber and H. Yserentant, Multilevel methods for elliptic problems on domains not resolved by the coarse grid. Contemp. Math. 180 (1994) 49–49. [CrossRef] [Google Scholar]
  27. R. Kornhuber and H. Yserentant, Numerical homogenization of elliptic multiscale problems by subspace decomposition. Multiscale Model. Simul. 14 (2016) 1017–1036. [Google Scholar]
  28. R. Kornhuber, D. Peterseim and H. Yserentant, An analysis of a class of variational multiscale methods based on subspace decomposition. Math. Comput. 87 (2018) 2765–2774. [Google Scholar]
  29. M.R. Lancia, A transmission problem with a fractal interface. Zeitschrift für Analysis und ihre Anwendungen 21 (2002) 113–133. [CrossRef] [MathSciNet] [Google Scholar]
  30. A. Målqvist and D. Peterseim, Localization of elliptic multiscale problems. Math. Comput. 83 (2014) 2583–2603. [Google Scholar]
  31. U. Mosco and M.A. Vivaldi, Layered fractal fibers and potentials. Journal de Mathématiques Pures et Appliquées 103 (2015) 1198–1227. [CrossRef] [MathSciNet] [Google Scholar]
  32. H. Nagahama and K. Yoshii, Scaling laws of fragmentation. In: Fractals and Dynamic Systems in Geoscience. Springer (1994) 25–36. [CrossRef] [Google Scholar]
  33. O. Oncken, D. Boutelier, G. Dresen and K. Schemmann, Strain accumulation controls failure of a plate boundary zone: linking deformation of the central andes and lithosphere mechanics. Geochem. Geophys. Geosyst. 13 (2012) Q12007. [CrossRef] [Google Scholar]
  34. P. Oswald, On a BPX-preconditioner for P1 elements. Computing 51 (1993) 125–133. [CrossRef] [MathSciNet] [Google Scholar]
  35. D. Peterseim, Variational multiscale stabilization and the exponential decay of fine-scale correctors. In: Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Springer (2016) 343–369. [CrossRef] [Google Scholar]
  36. E. Pipping, R. Kornhuber, M. Rosenau and O. Oncken, On the efficient and reliable numerical solution of rate-and-state friction problems. Geophys. J. Int. 204 (2016) 1858–1866. [CrossRef] [Google Scholar]
  37. J. Podlesny, Multiscale modelling and simulation of deformation accumulation in fault networks. Ph.D. thesis, Freie Universität Berlin (2022) [Google Scholar]
  38. T. Preusser, M. Rumpf, S. Sauter and L.O. Schwen, 3D composite finite elements for elliptic boundary value problems with discontinuous coefficients. SIAM J. Sci. Comput. 33 (2011) 2115–2143. [Google Scholar]
  39. J.B. Rundle, D.L. Turcotte, R. Shcherbakov, W. Klein and C. Sammis, Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems. Rev. Geophys. 41 (2003). DOI: 10.1029/2003RG000135. [Google Scholar]
  40. C.G. Sammis, R.H. Osborne, J.L. Anderson, M. Banerdt and P. White, Self-similar cataclasis in the formation of fault gouge. Pure Appl. Geophys. 124 (1986) 53–78. [CrossRef] [Google Scholar]
  41. L.N. Slobodecki, Generalized Sobolev spaces and their application to boundary problems for partial differential equations. Leningrad. Gos. Ped. Inst. Ucen. Zap 197 (1958) 54–112. [Google Scholar]
  42. H. Triebel, Theory of Function Spaces. Birkhäuser Basel (1983). [CrossRef] [Google Scholar]
  43. D.L. Turcotte, Crustal deformation and fractals, a review. In: Fractals and Dynamic Systems in Geoscience, edited by J.H. Kruhl. Springer (1994) 7–23. [CrossRef] [Google Scholar]
  44. D.L. Turcotte, Fractals and Chaos in Geology and Geophysics. Cambridge University Press (1997). [Google Scholar]
  45. R. Verfürth, Error estimates for some quasi-interpolation operators. ESAIM: M2AN 33 (1999) 695–713. [CrossRef] [EDP Sciences] [Google Scholar]
  46. E. Weinan and B. Engquist, The heterognous multiscale methods. Commun. Math. Sci. 1 (2003) 87–132. [CrossRef] [MathSciNet] [Google Scholar]
  47. J. Xu, Iterative methods by space decomposition and subspace correction. SIAM Rev. 34 (1992) 581–613. [CrossRef] [MathSciNet] [Google Scholar]
  48. J. Xu and Y. Zhu, Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients. Math. Models Methods Appl. Sci. 18 (2008) 77–105. [CrossRef] [MathSciNet] [Google Scholar]
  49. H. Yserentant, Old and new convergence proofs for multigrid methods. Acta Numer. 2 (1993) 285–326. [CrossRef] [Google Scholar]
  50. V.V. Zhikov and A.L. Pyatnitski, Homogenization of random singular structures and random measures. Izvestiya Rossi skaya Akademiya Nauk. Seriya Matematicheskaya 70 (2006) 23–74. [CrossRef] [Google Scholar]

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