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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1433-1453
  • MSC: Primary 65M60; Secondary 35Q99, 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-1995-1308451-4
  • MathSciNet review: 1308451