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Odd order governing equation - FE formulation

ramdas chennamsetti's picture

Hi!!

We generally encounter governing equations of even order. In FE formulation we get a symmetric coefficient matrix 'A' (AX = B). I have a few doubts as follwing.

[a] Any odd order governig equations ? If so, you may please write.

[b] Say, it has a functional also, then, what's the order of that differentiation?

[c] For even order (n) differential equations (DE), when we use weak formulation approach, we bring down the order to n/2. This  finally gives us a symmetric coefficients matrix 'A' (weighting function and shape function are same). But, for odd order DE, when weak formulation is used, then, what's the reduction in the order. I think it may not be n/2.

You may plese throw some light on the above questions.

- Ramdas

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