Adaptive Methods for Parameter Identification in Ground Water Hydrology

Beitrag in einer Fachzeitschrift
(Online-Publikation)


Details zur Publikation

Autorinnen und Autoren: Hoffmann KH, Knabner P, Seifert W
Zeitschrift: Advances in Water Resources
Jahr der Veröffentlichung: 1991
Band: 14
Heftnummer: 5
Seitenbereich: 220-239
ISSN: 0309-1708
Sprache: Englisch


Abstract

The
paper considers the simultaneous identification of parameters and
source term appearing in elliptic Partial Differential Equations from
knowledge of the reference potential, which satisfies Dirichlet boundary
conditions. Identifying the unknowns means complying with the equation
error criterion. The adaptive method consists of transforming both the
potential and the unknown parameters into time-dependent quantities,
which evolve according to given laws. In the continuum case, the time
decay property of a Lyapunov function is shown to hold.

Next, the
finite-dimensional (Galerkin) approximation of the evolution equations
is considered and, given the existence of a solution, the pertaining
convergence results are stated s. t., the time-dependent potential
approaches the reference potential and the unknowns asymptotically
comply with the time-independent equation.

Then, the discrete
identification problem is stated. The finite element method is used to
obtain the discrete equation error criterion. A Eulerian numerical
scheme for all discretized evolution equations is provided. The
sequences of the corresponding solutions i. e., the potential and the
unknowns, are shown to converge. The detailed proof is provided.

Finally,
the above method is applied to the identification of hydraulic
conductivity, leakage parameter and source term of a two-layered aquifer
in the Aachtal (Germany) area. The numerical results obtained from
noiseless and noisy potential data are provided.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Knabner, Peter Prof. Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Einrichtungen weiterer Autorinnen und Autoren

Technische Universität München (TUM)
Universität Augsburg


Zitierweisen

APA:
Hoffmann, K.-H., Knabner, P., & Seifert, W. (1991). Adaptive Methods for Parameter Identification in Ground Water Hydrology. Advances in Water Resources, 14(5), 220-239. https://dx.doi.org/10.1016/0309-1708(91)90036-N

MLA:
Hoffmann, Karl-Heinz, Peter Knabner, and Wolfgang Seifert. "Adaptive Methods for Parameter Identification in Ground Water Hydrology." Advances in Water Resources 14.5 (1991): 220-239.

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