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PDE (Weak, Coefficient and General Form)

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Hi

I was reading literature on PDE (all three forms) and I found General (or coefficient) form is much easier to use than the weak one. I was wondering if there are anythings which we cannot perform using General/coefficient form and we must use weak form? Or we can do all what we want via an easier formulation?
As an example, if I want to modify the built-in continuity, momentum equation-we can simply make changes in "gamma" and "f" using general form which will be much easier instead of formulating a new continuity, momentum equation using weak form.
I want to know whether there are any limitations in using general form and we must take help from the weak form?

regards
Naveed

4 Replies Last Post 13.02.2012, 11:51 GMT-5

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Posted: 10 years ago 09.04.2010, 03:41 GMT-4
your question is profound and interresting.

weak form has proven itself to be the NATURAL way to write PDE [ going back to distribution theory] and finite element codes in fact start from the weak form to provide numerical solution.

The powerful trick with weak form is , becasue of "integration by part" formula [ they have fancier name dimensions higher than 1 you can couple in an easy way the behaviour of a soliution in a domain on boundaries on point and so forth... and you can deal with some singularities in a numerically sensitive and robust way

One example is poisson equation with a point source that or impact loading.. that are discussed as part of comsol sample model or in a thread in this forum.... you can do things in a more natural way... but true you dont always need it too

So Could you do without it? MAybe I am not an expertenough in Comsol specifically
BUT if you make the effort to learn it you will find it natural and simple and powerful indeed.

I understand there are other benefits in the way comsol conpute the solution [ just reading the doc]
but I dont have enough experience in using cosol specifically to comment on that
JF
your question is profound and interresting. weak form has proven itself to be the NATURAL way to write PDE [ going back to distribution theory] and finite element codes in fact start from the weak form to provide numerical solution. The powerful trick with weak form is , becasue of "integration by part" formula [ they have fancier name dimensions higher than 1 you can couple in an easy way the behaviour of a soliution in a domain on boundaries on point and so forth... and you can deal with some singularities in a numerically sensitive and robust way One example is poisson equation with a point source that or impact loading.. that are discussed as part of comsol sample model or in a thread in this forum.... you can do things in a more natural way... but true you dont always need it too So Could you do without it? MAybe I am not an expertenough in Comsol specifically BUT if you make the effort to learn it you will find it natural and simple and powerful indeed. I understand there are other benefits in the way comsol conpute the solution [ just reading the doc] but I dont have enough experience in using cosol specifically to comment on that JF

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Posted: 10 years ago 09.04.2010, 04:03 GMT-4
Hi Jean

Thanks for the reply. Indeed you are correct, when we need to go into complexity such as special boundary conditions, then we must take help from weak form, as I beleive general form could be limited or difficult to handle in that sense.

Regards
Naveed
Hi Jean Thanks for the reply. Indeed you are correct, when we need to go into complexity such as special boundary conditions, then we must take help from weak form, as I beleive general form could be limited or difficult to handle in that sense. Regards Naveed

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Posted: 9 years ago 07.01.2011, 07:32 GMT-5
Hi all,

I come back here because I have some question about Weak form
Boundary.

I have a boundary integral equation int_{boundary)u(s)=-u(s).
I use the Weak form boundary to find the unknown u(s) definined at
the surface of the geometry.

Brievely, how does comsol do to solve it by using FEM.
I think that comsol just expand the solution u in a shape functions set
then solve the equation system obtained for each node of the mesh.
I am right ? How does play the test function ?
Someone can explain to me the different steps
used by comsol to solve a problem using
Weak form boundary ?

Thank you very much !

Sullivan
Hi all, I come back here because I have some question about Weak form Boundary. I have a boundary integral equation int_{boundary)u(s)=-u(s). I use the Weak form boundary to find the unknown u(s) definined at the surface of the geometry. Brievely, how does comsol do to solve it by using FEM. I think that comsol just expand the solution u in a shape functions set then solve the equation system obtained for each node of the mesh. I am right ? How does play the test function ? Someone can explain to me the different steps used by comsol to solve a problem using Weak form boundary ? Thank you very much ! Sullivan

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Posted: 8 years ago 13.02.2012, 11:51 GMT-5
Hi Naveed:

According to my understanding, the weak form PDE are suitable for solving coupled equations.
Hi Naveed: According to my understanding, the weak form PDE are suitable for solving coupled equations.

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