Finite Element Method vs. Integrated Finite Difference for Complex Geometries

[bzz77]

Hello all:

For modeling flow (or whatever) in a non-rectangular geometry, can anyone comment on whether the finite element method would be better or worse or the same as the integrated finite difference method?

I'm reading some papers by competing groups (so I can decide which code to start using), and the finite element group maintains that the flow field can be distorted when using the integrated finite difference method.

My questions: first of all, is this true? If so, is the problem significant? And are there any other potential advantages/disadvantages of either method over the other?

I have basic knowledge of these methods, but not enough to evaluate their advantages/disadvantages in a meaningful way! Thanks.

 

[Studiot]

For fluid modelling, boundary element methods often have significant calculation advantage over either FE or FD methods.

The problem with a FD method is that it is an extrapolation method for which errors can rapidly propagate and grow in the wrong circumstances.


The FE method is an interpolation method which limits this problem

go well

 

[bzz77]

Thanks Studiot. I'll look into that.

Right now my choice is between integrated finite difference and finite element though. Thanks again.

 

[Studiot]

For the FD method I can recommend

Numerical Solution of Partial Differential Equations: Finite Difference Methods

GD Smith

Oxford

 

[bzz77]

Thanks a lot, Studiot.

 

[Studiot]

Further bibliography

Brebbia has written several books about the boundary element method, including comparisons with FE/FD, working problems both ways.

Boundary elements for engineers

Elements of Computational Hydraulics by

Koutitas

Compares both FD and FE methods with many practical examples.

 

[bzz77]

Thanks again for going to so much trouble, Studiot. I'll definitely look that up. So far the only comparisons of FE and integrated FD I can find are by the competing groups, and I need something objective. Appreciate it.