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Mathematics of Computation

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A finite element model for the time-dependent Joule heating problem

Authors: Charles M. Elliott and Stig Larsson
Journal: Math. Comp. 64 (1995), 1433-1453
MSC: Primary 65M60; Secondary 35Q99, 65N30
MathSciNet review: 1308451
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Abstract: We study a spatially semidiscrete and a completely discrete finite element model for a nonlinear system consisting of an elliptic and a parabolic partial differential equation describing the electric heating of a conducting body. We prove error bounds of optimal order under minimal regularity assumptions when the number of spatial variables $d \leq 3$. We establish the existence of solutions with the required regularity over arbitrarily long intervals of time when $d \leq 2$.

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Keywords: Joule heating, nonlinear, elliptic, parabolic, finite element, backward Euler, existence, regularity
Article copyright: © Copyright 1995 American Mathematical Society