In article <Pine.GSO.3.96.1000419234628.6765Aemail@example.com>, John Hernlund <firstname.lastname@example.org> wrote: > On Wed, 12 Apr 2000, Mirko Vukovic wrote: > > John Hernlund <email@example.com> wrote: > > > Hello There, > > > I have been reading a lot of literature on the finite difference > > and finite > > > element methods recently and have found a great variety of opinions > > regarding > > > which is best for this or that problem. In programming both types I > > have > > > found that both can produce nice results. I would like to hear more > > opinions > > > on the matter however... > > > > > > What do you think? > > I thing I am quoting here from the literature on simulation of wave > > propagation in magnetized plasmas (ionized gas) which I read years ago. > > > > These problems in general have pairs of solutions, one growing, one > > damping. In order to make sure that the growing one does not over-whelm > > the solution, one is supposed to use finite elements. I presume that > > the reason is that when you convert the PDE into a variational form, you > > take the boundary conditions into account, and thus suppress the > > un-physical solution. > > You can accomplish this with finite differences also. In our PDE class we > took the fourier transform of a modified difference scheme which had a > diffusion term and adjusted the parameters to obtain the correct decay and > dispersion for the waves. After that, everything ran just fine... As a > matter of fact, controlling these things in finite differences was far easier > than for finite elements. > Could you point me to a reference that deals with that example? I would like to take a look.