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Old   August 17, 2012, 14:23
Question Question about FEM theory
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lnk
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Hi everyone,

May I ask a question about FEM theory? Why we multiply the residual with a weighting function? Why we don't just minimize the residual?

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Old   August 17, 2012, 16:20
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Originally Posted by lnk View Post
Hi everyone,

May I ask a question about FEM theory? Why we multiply the residual with a weighting function? Why we don't just minimize the residual?

Best,
lnk
you can also use the same residual as weighting function ... it depends on the projection you want to use
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Old   August 17, 2012, 16:31
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Originally Posted by FMDenaro View Post
you can also use the same residual as weighting function ... it depends on the projection you want to use
Thanks. What do you mean by projection? Does that mean the weighting function is used to make the minimization equation easier to solve?


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Old   August 17, 2012, 16:45
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Thanks. What do you mean by projection? Does that mean the weighting function is used to make the minimization equation easier to solve?


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lnk

as "projection" I mean the integral of the product of the two functions.
The choice of the test-functions is quite general, you can see also spectral methods and finite volume methods as particular derivation of a specific choice
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Old   August 17, 2012, 17:01
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Originally Posted by FMDenaro View Post
as "projection" I mean the integral of the product of the two functions.
The choice of the test-functions is quite general, you can see also spectral methods and finite volume methods as particular derivation of a specific choice
But won't we have better result ( lowest integrated residual ) if we only minimize the integrated residual without multiplying the residual with weighting function?
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Old   August 17, 2012, 17:19
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But won't we have better result ( lowest integrated residual ) if we only minimize the integrated residual without multiplying the residual with weighting function?
If I remember, the method of simply integrate the residual is the Ritz method...
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Old   August 17, 2012, 17:26
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I extracted a page, hoping that can help you
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