Hi, what are the basic advantages of finite elements method in comparison with finite differences method? Thanks.

The most considerable advantage of FEM is its great strength in the modeling of complex geometries.

I think question is FEM vs FVM as all major codes are FVM. From user point of view FVM can handle complex geometry as easy as FEM.

I don't know much about FVM but my very naive idea about this method tells me that FVM works with balance fluxes through the element faces while FEM works with interpolation and trial functions applied to the problem and integrated over the computational domain.

For FEM and FVM enthusiasts there is a formulation called CVFEM (Control Volume Finite Element Method) where some FEM and FVM properties are combined to produce a new approach that summarizes the main advantages of both methods (complex geometries and conservation properties, etc...).

I've been work with FEM but I could say that FVM is more "traditional" in the CFD's world. Most of FVM researchers point that FEM is not locally conservative for CFD problems, but this problem was already overcame by Hughes and co-workers recently (I'll post the complete reference for this subject later). It's an old and very fruitful source of discussion (and fighting...) among FEM and FVM - CFD researchers.

Regards

Renato.

This is an old and recurring debate. Both FEM and FVM are good for problems with complex geometry. If you are interested in only second order schemes, then FVM is good. But going to higher order with FVM on unstructured grids is costly. FEM provides a better framework for this since you can also do p-adaptation, ie., locally increase the order of the basis functions. Recent schemes like Discontinuous Galerkin FEM and Spectral Volume/Difference schemes lie in between FEM and FVM and appear to be very attractive for higher order simulations necessary for LES/DNS on unstructured grids.

I have heard that solution speed is the main reason fvm is prefered. Anybody have a comparison between fvm (fluent, starcd, cfx, icepak, flotherm, cfdace, floworks) and fem (fidap, cfdesign)?