Hi,

Is there anyone who is aware of advantages and drawbacks of penalty finite elment methods? especially when applied to unsteady, time-dependent stokes flows? Is the method a good one?

I did not find much pertinet reference. Any information (e.g., papers) and discussion is highly appreciated.

Hansong

I heard this term for many times but don't know what it really is. however, another term "lagrange multiplier " often accompanies the FE with penalty, could you search that?

also, you may look up books written by J.T. Oden( finite elements, 6 volumes, 1980s), O.C. Zienkiewicz(2000, three volumes), or J.N. Reddy ( two books, an troduction to ..., or FEM in fluids and heat transfer)

they are some of best researchers and writers in this subject.

for nonlinear problem or skew-symmeric operators,stabilzed version of FEm, such as, SUPG is better( streamline upwind petrov galerkin). stokes flow is linear and diffusion dominated( am I wrong? I have to look up fluid text book), then stability is not an issue, and all FEMs work well generally. but what kind of trouble will unsteady bring into FEM approach? I don't know.

Thanks for your response.

I have checked one of Zienkiewicz's early books and one of Reddy's books and some papers, there is not much discussion about the question in them.

A major negative side of the method could be that, as some references indicate, the introduction of a penalty term will lead to a ill-conditioned system that is difficult to sovle. To me it is not clear that if this drawback is fatal.

Also, it seems that the literature about unstaedy problem using the penalty method (or lagrange multiplier) is sparse.