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Re: Finite Difference vs. Finite Element
Posted:
Apr 21, 2000 11:06 AM
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In article <Pine.GSO.3.96.1000419234628.6765A-100000@general5.asu.edu>,
John Hernlund <hernlund@imap3.asu.edu> wrote:
> On Wed, 12 Apr 2000, Mirko Vukovic wrote:
> > John Hernlund <hernlund@imap3.asu.edu> 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.
Thanks,
(Now curious) Mirko
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