Hi is the finite element more accurate than the finite volum mehthod with the same number of cell

it is well known that the finite element techniques is the most accurate numerical solution technique ever. But there is no exact problem in my hand now.

Not exactly true. In the special cases where they are applicable spectral/Galerkin methods are more accurate.

Strictly Speaking the finite volume method is a special case of element method - see for example the book "Computational fluid dynamics" by Chung which discusses FDM, FVM and FEM methods in detail.

Well if the solution you are looking for is flat(read very smooth), in other words 0-order(read low order), yes then finite volumes will be more efficient as a special case of the general higher order finite elements(eg Discontinuous Galerkin).

I am not trying to start the eternal discussion on which is better, just as I try to avoid Windows-Linux, vi-emacs , ... discussions.

This reply just in response as a note on the side to the reply of Tom, who reacted on the side note of B. R. Guirguis in true 'Fermat style'.

Isn t the discontinuous galerkin methods part of the finite volume schemes? By High order finite volume scheme, do you mean godunov finite volume method? Sadek