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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