Summer School Utrecht,

1
Homogenization Theory Sabine Attinger
2
Schedule
3
Literature

• 1. Motivation and Basic Ideas
• Pavliotis,G., Homogenization Theory for
  Partial Differential Equations, Lecture Notes,
  Chapter 1, 2005
• http//www.ma.ic.ac.uk/pavl/ch1.pdf
• Hornung U., Homogenization and Porous Media,
  Springer, 1997.
• G. Papanicolaou, Diffusion in Random Media,
  In Surveys in Applied
• Mathematics, edited by J.B.Keller,
  D.McLaughlin and G.Papanicolaou, Plenum Press,
  pp. 205-255, 1995.
• 2. Elliptic Equations Derivation of Homogenized
  Equations
• Pavliotis,G., Homogenization Theory for
  Partial Differential Equations, Lecture Notes,
  Chapter 2, 2005
• http//www.ma.ic.ac.uk/pavl/ch2.pdf
• 3. Elliptic Equations Calculation of effective
  coefficients
• Pavliotis,G., Homogenization Theory for
  Partial Differential Equations, Lecture Notes,
  Chapter 2, 2005
• http//www.ma.ic.ac.uk/pavl/ch2.pdf

4
Literature

• 4. Elliptic Equations HT in comparison with
  other upscaling methods
• Gelhar, L. W., Stochastic Subsurface Hydrology,
  Prentice Hall,1993
• Dagan, G., Solute transport in heterogeneous
  porous formations, J. Fluid Mech. 145, 151-177,
  1984.
• Rubin, Y., Applied Stochastic Hydrogeology,
  Book News, Inc., Portland, 2003
• Zhang, D., Stochastic Methods for Flow in
  Porous Media Coping With Uncertainties, Academic
  Press, San Diego, CA, 2002
• Whitaker, S., The Method of Volume Averaging,
  Kluver Academic
• Press, Dordrecht, 1999.
• Attinger, S., Generalized Coarse Graining
  Procedures in Heterogeneous Porous Media,
  Computational Geosciences ,Vol 7, No 4, 253-273,
  2003
• Attinger, S., Multiscale Modelling in
  Subsurface Hydrology, Habilitationsschrift, 2004

5
Literature

• 5. Elliptic Equations Numerical Homogenization
• G. Allaire, Introduction to Multiscale Finite
  Element Methods, 2005
• http//www.cmap.polytechnique.fr/allaire/mul
  timat/allaire_lecture.pdf
• Pavliotis,G., Homogenization Theory for
  Partial Differential Equations, Lecture Notes,
  Chapter 3-5, 2005
• http//www.ma.ic.ac.uk/pavl/ch3.pdf
• http//www.ma.ic.ac.uk/pavl/ch4.pdf
• http//www.ma.ic.ac.uk/pavl/ch5.pdf
• Hou , T.Y. and X. Wu, A Multiscale Finite
  Element Method for Elliptic Problems in Composite
  Materials and Porous Media, Journal of
  Computational Physics, 134, 169189 (1997)
• Hou , T.Y., X. Wu and Z. Cai, Convergence of
  a Multiscale Finite Element Method for Elliptic
  Problems with rapidly ocsillating coefficients,
  Mathematics of Computation, Volume 68, Number
  227, 913-943,1999
• Ming, P. and X. Yue, Numerical methods for
  multiscale elliptic problems, Journal of
  Computational Physics 214 , 421445, 2006

6
Literature

• 6. HT of other equations, e.g advection-diffusion
  equations
• Pavliotis,G., Homogenization Theory for
  Partial Differential Equations, Lecture Notes,
  Chapter 6, 2005
• http//www.ma.ic.ac.uk/pavl/ch6.pdf
• Lunati, I., S. Attinger and W. Kinzelbach,
  Macrodispersivity for transport in arbitrary
  nonuniform flow fields Asymptotic and
  preasymptotic results, Water Resour. Res., Vol
  38, No.10, 1187,2002.