[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

[FMDenaro]

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

[lnk]

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

[FMDenaro]

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

[lnk]

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?

[FMDenaro]

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...

[FMDenaro]

I extracted a page, hoping that can help you