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A free boundary value problem for water invading an unsaturated medium

Ein freies Randwertproblem für das Eindringen von Wasser in ein ungesättigtes Medium

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Abstract

We discuss a mathematical model arising in the filtration of a fluid through a porous medium. The model leads to a free boundary value problem whose governing equation depends on the retention function. A numerical approximation by means of finite elements is used to obtain an existence and uniqueness theorem along with an error estimate for a linear retention function.

Zusammenfassung

Wir diskutieren ein mathematisches Modell für die Filterung einer Flüssigkeit durch ein poröses Medium. Das Modell führt auf ein freies Randwertproblem, dessen Gleichung von der Retentionsfunktion abhängt. Mit Hilfe einer numerischen Finite-Elemente-Approximation werden ein Existenz- und Eindeutigkeitssatz sowie Fehlerabschätzungen für den Fall einer linearen Retentionsfunktion hergeleitet.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia

    A. Kharab

  2. Department of Mathematics, Oregon State University, 97330, Corvallis, OR, USA

    R. B. Guenther

Authors
  1. A. Kharab
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  2. R. B. Guenther
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Kharab, A., Guenther, R.B. A free boundary value problem for water invading an unsaturated medium. Computing 38, 185–207 (1987). https://doi.org/10.1007/BF02240095

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