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Basic question about writing a differential equation related to finite element

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Old   April 9, 2014, 08:12
Default Basic question about writing a differential equation related to finite element
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I'm writing a code to solve differential equations using a finite element method. I need to write a report about my activities. I know I should know this, but I'm getting confused about how to write a general differential equation in this situation. I have tried Google, but no luck. I would really appreciate some help. This is not a homework question; I'm an old fart and it has been a while since I did this stuff!

I know that when a variable is constant, it should go outside of the differential. For example, if k is constant, an equation should be written as q = k (dT/dx). But when using numerical methods, k might be constant within one time-step, but change for the next time step. So does this mean k needs to go inside the differential?

For example, in my code, there are several calculation steps in each time step. There is a calculation that changes k, then there are additional calculations to change other variables (all using the new k); q is calculated using the new k. Then we go to a new time-step and k changes again.
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Old   April 10, 2014, 03:50
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Marek Chodorski
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Hi,
Your equation should look like this:
http://feazone.org/readarticle.php?article_id=11
Regards,
Marek
PS Description is in polish
use google translator - the sense should be understandable - I hope
In your case T is temperature ( I guess ) in my S is concentration
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