On the box method for a non-local parabolic variational inequality

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2001, 1(1): 71-88. doi: 10.3934/dcdsb.2001.1.71

On the box method for a non-local parabolic variational inequality

Walter Allegretto ^1, , Yanping Lin ^2, and Shuqing Ma ^1,

1.	Department of Mathematical Sciences, University of Alberta, Edmonton A B, Canada T6G 2G1
2.	Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1, Canada

Received September 2000 Revised November 2000 Published January 2001

Abstract
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In this paper we study a box scheme (or finite volume element method) for a non-local nonlinear parabolic variational inequality arising in the study of thermistor problems. Under some assumptions on the data and regularity of the solution, optimal error estimates in the $H^1$-norm are attained.

Keywords: Box methods, non-local, thermistor and variational inequality..

Mathematics Subject Classification: 76S0.

Citation: Walter Allegretto, Yanping Lin, Shuqing Ma. On the box method for a non-local parabolic variational inequality. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 71-88. doi: 10.3934/dcdsb.2001.1.71

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