A finite element weighted residual solution to one‐dimensional field problems

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Abstract
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.

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