CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
-   Main CFD Forum (https://www.cfd-online.com/Forums/main/)

 lnk August 17, 2012 14:23

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

 FMDenaro August 17, 2012 16:20

Quote:
 Originally Posted by lnk (Post 377540) 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

 lnk August 17, 2012 16:31

Quote:
 Originally Posted by FMDenaro (Post 377551) 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

 FMDenaro August 17, 2012 16:45

Quote:
 Originally Posted by lnk (Post 377556) 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

 lnk August 17, 2012 17:01

Quote:
 Originally Posted by FMDenaro (Post 377558) 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?

 FMDenaro August 17, 2012 17:19

Quote:
 Originally Posted by lnk (Post 377561) 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...

 FMDenaro August 17, 2012 17:26

1 Attachment(s)