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 August 17, 2012, 14:23 Question about FEM theory #1 Senior Member   lnk Join Date: Feb 2011 Location: Switzerland Posts: 118 Rep Power: 8 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

August 17, 2012, 16:20
#2
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Filippo Maria Denaro
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Quote:
 Originally Posted by lnk 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

August 17, 2012, 16:31
#3
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lnk
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Quote:
 Originally Posted by FMDenaro 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?

Best,
lnk

August 17, 2012, 16:45
#4
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Filippo Maria Denaro
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Quote:
 Originally Posted by lnk Thanks. What do you mean by projection? Does that mean the weighting function is used to make the minimization equation easier to solve? Best, 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

August 17, 2012, 17:01
#5
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lnk
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Quote:
 Originally Posted by FMDenaro 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?

August 17, 2012, 17:19
#6
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Filippo Maria Denaro
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Quote:
 Originally Posted by lnk 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...

August 17, 2012, 17:26
#7
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Filippo Maria Denaro
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