Int. J. Numer. Anal. Mod., 4 (2007), pp. 519-530.


On an interface problem with a nonlinear jump condition, numerical approximation of solutions

G. Hetzer 1, A. J. Meir 1

1 Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA

Received by the editors February 20, 2006, and, in revised form, March 3, 2006
Abstract

In this paper we describe a one-dimensional interface problem for the heat equation, with a nonlinear (quadratic) jump condition at the interface. We derive a numerical method for approximating solutions of this nonlinear problem and provide some results from numerical experiments. The novelty of this problem is precisely this nonlinear (quadratic) jump condition, and it arises in the study of polymeric ion-selective electrodes and ion sensors.

AMS subject classifications: 35K55, 35K60, 35Q80, 35R05, 65M60
Key words: interface problem; jump condition; ion-selective electrodes
Email: hetzege@auburn.edu (G. Hetzer), ajm@auburn.edu (A. J. Meir)
 

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