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PDE (Weak, Coefficient and General Form)
Posted 2010/04/09 2:58 GMT-4 Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 3.5a, Version 4.0 4 Replies
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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
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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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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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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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According to my understanding, the weak form PDE are suitable for solving coupled equations.