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Convergence of a numerical method in mathematical spontaneous potential well-logging

Published online by Cambridge University Press:  26 September 2008

Yi Zhou  and
Zhijie Cai
Yi Zhou
Affiliation:
Institute of Mathemtics, Fudan University, Shanghai 200433, P.R. China
Zhijie Cai
Affiliation:
Institute of Mathemtics, Fudan University, Shanghai 200433, P.R. China
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Abstract

Spontaneous potential well-logging is an important technique in petroleum exploitation. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on interfaces. At the joint points of the interfaces, the jumps of the spontaneous potential do not, in general, satisfy the compatibility condition. It turns out that it is impossible to find a piecewise H1 solution to the problem, and the standard finite element method cannot be applied to get an approximate solution. In this paper, by means of a new method, we prove that the problem exists a unique piecewise solution for some p < 2. We give an estimate for the solution as well. This allows us to prove the convergence of a numerical scheme proposed in [3].

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 1 , February 1996 , pp. 31 - 41
Copyright
Copyright © Cambridge University Press 1996

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References

[1] Ta-tsien, Li, Yong-ji, Tan & Yue-jun, Peng 1994 Mathematical model and method for the spontaneous potential well-logging. Euro. J. Appl. Math. 5, 123–139.CrossRefGoogle Scholar
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[4] Hailong, Li 1994 Theoretical foundation of the numerical methods for the SP well-logging. Chin. Ann. Math. Ser. A, 15(3), 262–269.Google Scholar
[5] Yazhe, Chen & Lancheng, Wu 1991 Second Order Elliptic Equations and Systems. Scientific Publisher.Google Scholar
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