In a finite volume CFD package numerical diffusion can be minimised by using a higher-order discretisation scheme. What can I do if I work in a finite element model with a triangular mesh where I obvisously have no choice on the order of differencing scheme as the method of the weighted residual applies.

In FEM higher order accuracy is obtained by using higher order basis functions and elements, quadratic and above.

Thanks for the prompt response. I know this is gonna be a tricky one, but what's usually(!) the order of a basis function? Is it higher than 5th order?

That usually depends on how accurate you want your results. If you can use more grid points (h-refinement) you can use lower order basis functions while if you want to reduce the number of grid points you have to use higher order basis functions(p-refinement). Sometimes a combination is used. The lowest order basis is also dictated by the order of the governing equations. For NS equations which contain second derivatives the weak formulation used in FEM will contain first derivatives so that at-least linear basis functions are required.

Thanks for your help. I would like to take this to one step further by first returning to my initial message and ask you: If you had a hex element in a finite diffence scheme (truncated after first term in Taylor-series) and a tet element in a finite element scheme, which one would give you more accurate results (assuming same area and material properties)? Is it gonna be the FD due to the fact that numerical diffusion is gonna be minimised in a hex element or is it gonna be the FE because the weighted residuals with the higher basis function outweigh numerical diffusion?