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Consistent use of finite elements in time and the performance of various recurrence schemes for the heat diffusion equation
Author(s) -
Bettencourt J. M.,
Zienkiewicz O. C.,
Cantin G.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620170609
Subject(s) - reinterpretation , context (archaeology) , finite element method , forcing (mathematics) , feature (linguistics) , mathematics , boundary value problem , term (time) , heat equation , diffusion , domain (mathematical analysis) , oscillation (cell signaling) , spacetime , mathematical analysis , physics , engineering , structural engineering , paleontology , linguistics , philosophy , genetics , quantum mechanics , acoustics , biology , thermodynamics
Abstract The use of the finite element concept in the time domain has resulted in a reinterpretation of many previously recorded recurrence formulae and the discovery of new ones. An important new feature common to all such schemes is the fact that a weighted forcing term is used. This precludes the application of unrealistic forcing terms resulting in a direct finite difference derivation and ‘smooths’ oscillation due to sudden changes of boundary condition. This problem is discussed in the context of various two‐ and three‐level time schemes.