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

Pages: 71 - 88, Volume 1, Issue 1, February 2001      doi:10.3934/dcdsb.2001.1.71

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Walter Allegretto - Department of Mathematical Sciences, University of Alberta, Edmonton A B, Canada T6G 2G1, Canada (email)
Yanping Lin - Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1, Canada (email)
Shuqing Ma - Department of Mathematical Sciences, University of Alberta, Edmonton A B, Canada T6G 2G1, Canada (email)

Abstract: 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:  76S05.

Received: September 2000;      Revised: November 2000;      Available Online: January 2001.