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Dispersion-based guidance for the temporal and spatial discretization of the one- and two-dimensional finite element solutions to the transient heat equation

✍ Scribed by W. Dauksher; A.F. Emery

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
371 KB
Volume
192
Category
Article
ISSN
0045-7825

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✦ Synopsis

Errors associated with the finite element solution to the transient heat equation are examined. These errors arise from the spatial and temporal discretizations chosen and are influenced by the shape of the thermal profile and the properties of the conducting medium. Since these errors alter the rate of heat diffusion, they are termed dispersive. A methodology for evaluating the numerically introduced dispersion is presented. Examples demonstrate that knowledge of the dispersion present in the numerical solution is useful in designing efficient and accurate finite element meshes.

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Finite differences and collocation metho
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✍ Jules Kouatchou πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 101 KB πŸ‘ 3 views

In this article, we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two-dimensional heat equation. We employ, respectively, second-order and fourth-order schemes for the spatial derivatives, and the discr