# American Institute of Mathematical Sciences

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

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

 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

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.
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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