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A means of solving ordinary and partial differential equations. The domain of the problem is broken up into elements, and the solution in each element is expanded in a basis of functions. The Finite Element Method lends itself well to adaptive refinement, irregular geometry, and good error estimates.

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When solving semi-discrete equations (originating from finite element models, for example), which are second-order in time of the form \begin{equation} M\ddot d + C\dot d + Kd = F, \end{equation} wher …
asked Jul 29 '15 by DanielRch
0
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Remember that when you multiply the strong-form equation by the shape function, the shape function is arbitrary. Therefore, by requiring that the residual be orthogonal to any such shape function, suc …
answered Nov 29 '14 by DanielRch
4
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If averaging the element fluxes, as suggested by @Bill Greene, does not produce accurate enough fluxes, there are ways to improve the accuracy of the fluxes by post-processing. A standard and quite st …
answered May 4 '17 by DanielRch
3
votes
It is a matter of boundary conditions on the longitudinal faces. As you noted, the axial stress and strain for a linear isotropic material will satisfy the following relation: \begin{equation} \sigma …
answered Apr 11 '18 by DanielRch
3
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There exist Absorbing Boundary Conditions for the wave equation that are stable and that go up to any order of accuracy (limited only by the accuracy of discretization of your model), so that they are …
answered Jul 25 '15 by DanielRch
1
vote
You are basically trying to solve a one-dimensional modified Helmholtz equation with variable coefficients. If the locations where the changes in the coefficients occur remain constant in time, I wo …
answered Dec 8 '14 by DanielRch