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A finite element weighted residual solution to one‐dimensional field problems
Author(s) -
Bruch John C.,
Zyvoloski George
Publication year - 1973
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.1620060413
Subject(s) - finite element method , mathematics , method of mean weighted residuals , galerkin method , mathematical analysis , convection–diffusion equation , representation (politics) , heat equation , mixed finite element method , extended finite element method , space (punctuation) , residual , term (time) , field (mathematics) , physics , computer science , algorithm , pure mathematics , quantum mechanics , politics , political science , law , thermodynamics , operating system
The one‐dimensional diffusion‐convection equation is formulated with the finite element representation employing the Galerkin approach. A linear shape function and two‐dimensional triangular and rectangular elements in space and time were used in solving the problem. The results are compared with finite difference solutions as well as the exact solution. As another example, the convective term is set equal to zero and these techniques are applied to the resulting heat equation and similar comparisons are made.