|
|
Re: Finite Difference vs. Finite Element
Posted:
May 28, 2004 11:01 AM
|
|
Saad wrote:
> Finite Difference method is far easier to implement
> than finite element method if one is developing a code himself.
I think that is a matter of opinion.
> The curved boundaries can be easily handled
> by the very general technique of numerical grid generation
> in which the irregualr domain is transformed into a regular domian
> along with the governing PDE which is then solved
> on this computational domain and the results transformed back.
> The main thing in this technique is that
> you don't have to know the transformation equations explicitily.
> Rather you assume them to be a solution of a PDE (usually Poisson's Eq.)
> and solve this numerically.
How is that "easier to implement" than the finite element method?
> Apart from this problem of irregular domains I do not much know about
> the inherent robustness and rigor of each method. However, it is to be
> noted that in the Finite Element method the error (Residue) is minimized
> at each point of the domain rather than at selected points (grid).
Please explain.
> Also, Finite Element Method gives you a continous solution
> over the whole domain, in contrast to The Finite Difference Method
> which gives the solution only on the grid points.
No.
Finite difference, finite element
and all other finite discretization methods are equivalent
for the same "quality of solution". Which means that
you end up solving the same equations
with the same computational complexity [efficiency].
The difference between the two methods seems to be
restricted entirely to the formulation of these equations.
Some people think that it is easier to formulate these equations
using the finite element method
when the geometry of the grid is irregular.
|
|
