How would you calculate the exact value of the truncation error? This is of course for finite element analysis using the forward finite difference method.(adsbygoogle = window.adsbygoogle || []).push({});

If your given a function u=u(x,t) and are to find the error at node (i,n+1), wouldn't you just take the difference between the value of the function and the value of the finite method?

So for example

u=u(x,t)=x*sin(t)

du/dt=x*cos(t)

finite difference method-time derivative:

[itex]\frac{\partial ^u}{\partial t}=\frac{u_i^{n+1}-u_i^n}{\Delta t}=\frac{x*sin(t+\Delta t)-x*sin(t)}{\Delta t}[/itex]

So therefore the exact error is...

[itex]x*cos(t)-\left[\frac{x*sin(t+\Delta t)-x*sin(t)}{\Delta t}\right][/itex]

However, if you were to plug in numbers for x, t, and [itex]\Delta t[/itex], I don't see a way of calculating an exact value for the truncation error. Is my thought process wrong?

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# Exact value of truncation error

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