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

Walter Allegretto; Yanping Lin; Shuqing Ma

doi:10.3934/dcdsb.2001.1.71

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2001, Volume 1, Issue 1: 71-88. Doi: 10.3934/dcdsb.2001.1.71

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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

Received: August 31, 2000

Revised: October 31, 2000

Published: January 2001

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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.

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Mathematics Subject Classification: 76S05.

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