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Hey! I need some help with this task!

Task: Derive variational formulation, finite element formulation, and time-marching scheme for problems (1a) - (1d).

I know how to solve the second derivative of x with finite element method but how do I solve the derivative of t (time)? Another question is that how to I solve it with the boundary conditions?

Thanks in beforehand!

Jacob Andreasson
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  • I have high suspicion that (1a) - (1d) are not individual tasks. Instead, I believe that (1a) is a PDE and the rest are its boundary and initial conditions. Is this the case? Also, if you want us to help solve something, please provide your own solution and show how far you got. Is this a problem from a course? Which workbook are you following? – Aleksejs Fomins Dec 02 '19 at 19:51
  • This is a task that we have gotten from the course! That is right that I should also written my solution but do you have any tips on how to fix the derivative of t (time)? – Jacob Andreasson Dec 02 '19 at 19:54
  • Can you explain what you mean by "solve" or "fix"? You said you know how to "solve" the second derivative wrt x. Can you explain what that means? Sorry for being picky, but your English is a little imperfect, so I need to make sure I understand exactly what you want – Aleksejs Fomins Dec 02 '19 at 19:58
  • The derivative by time is approximated, for example, as $\frac{u_i(t+\Delta t)-u_i(t)}{\Delta t}$. You know $u(x,0)$ from the boundary conditions so you can find $u_i(0+\Delta t)$ and so forth. That's the whole point of using finite elements, you start from the boundary and move layer by layer. – Vasili Dec 02 '19 at 20:49

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