Advertisement

Coefficient Identification in Elliptic Differential Equations

  • Ian Knowles
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 5)

Abstract

An outline is given for new variational approach to the problem of computing the (possibly discontinuous) coefficient functions p, q, and f in elliptic equations of the form —\( - \nabla \cdot \left( {p\left( x \right)\nabla u} \right) + \lambda q\left( x \right)u = f,\), x ∈ Ω ⊂ ℝ n , from a knowledge of the solutions u.

Keywords

Hydraulic Conductivity Inverse Problem Groundwater Flow Coefficient Function Elliptic Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Mary P. Anderson and William W. Woessner. Applied Groundwater Modeling. Academic Press, New York, 1992.Google Scholar
  2. [2]
    J. Bear. Dynamics of Fluids in Porous Media. American Elsevier, New York, 1972.zbMATHGoogle Scholar
  3. [3]
    J. Carrera. State of the art of the inverse problem applied to the flow and solute equations. In E. Custodio, editor, Groundwater Flow and Quality Modeling, pages 549–583. D. Reidel Publ. Co., 1988.CrossRefGoogle Scholar
  4. [4]
    J. Carrera and S.P. Neumann. Adjoint state finite element estimation of aquifer parameters under steady-state and transient conditions. In Proceedings of the 5th International Conference on Finite Elements in Water Resources. Springer-Verlag, 1984.Google Scholar
  5. [5]
    R.L. Cooley and R.L. Naff. Regression modeling of groundwater flow. In Techniques of Water-Resources Investigations, number 03-B4. USGS, 1990.Google Scholar
  6. [6]
    David Gilbarg and Neil S. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, New York, 1977.zbMATHCrossRefGoogle Scholar
  7. [7]
    Ian Knowles. Parameter identification for elliptic problems with discontinuous principal coefficients. preprint, 1997.Google Scholar
  8. [8]
    Ian Knowles and Robert Wallace. A variational method for numerical differentiation,. Numerische Mathematik, 70: 91–110, 1995.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    Ian Knowles and Robert Wallace. A variational solution of the aquifer transmissivity problem. Inverse Problems, 12: 953–963, 1996.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    W. Menke. Geophysical Data Analysis: Discrete Inverse Theory. Academic Press, New York, 1989.zbMATHGoogle Scholar
  11. [11]
    A. Peck, S.M. Gorelick, G. De Marsily, S. Foster, and V. Kovalevsky. Consequences of Spatial Variability in Aquifer Properties and Data Limitations for Groundwater Modeling Practice. Number 175. International Association of Hydrologists, 1988.Google Scholar
  12. [12]
    William W-G. Yeh. Review of parameter identification procedures in groundwater hydrology: The inverse problem. Water Resources Research, 22(2):95–108, 1986.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Ian Knowles
    • 1
  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA

Personalised recommendations