🚀 go-pugleaf

I will approach this from the perspective of using Galerkin methods for
approximating PDEs using fnite element techniques.

The Galerkin is an alternative formulation to the variational formulation
typically used when a variational does not exist.  If it is possible to integrate
the Galerkin form by parts one typically ends up with a variational formulation.

This statement has the following consequences:
 
     - a pure Galerkin formulatiuon typically results in nonsymmetric equations

     - a pure Galerkin forumlation typically requires trial functions of twiceUnread news in news.config                                 1 article  +  412 oldUnread news in news.config                                 1 article  +  412 old
            the order of an equivalent Variational formulation

There is also the issue that a Galerkin forumation, since it need not be
positive definite, can result in saddle solutions rather than the minima typical
of variational forms.  This has the effect in certain nonlinear PDEs for
introducing instability, although I am not aware of solid research to support
this statement for the general case,  It would  probably be an interesting
problem.  (Careful though, when evaluating convegence properties one should look
at the convergence of primary variables only, not secondary variables introduced
to enforce boundary conditions - e.g. one should not look at the convergence of
problems with Lagrange multiplier constraints by by including the behavior of the
Lagrange multipliers in the convergence study).

Hope this is useful!
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263