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

Elliott, Charles M.; Larsson, Stig

doi:10.1090/S0025-5718-1995-1308451-4

A finite element model for the time-dependent Joule heating problem
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by Charles M. Elliott and Stig Larsson PDF

Math. Comp. 64 (1995), 1433-1453 Request permission

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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