The volumes are the same as elements and cells.  They are largely tetrahedra in your case.  The mesh nodes are the corners of those tetrahedra.  In 3D they are NOT equal in number.  For all tetrahedra in the mesh, the ratio is roughly 5.5 elements/volumes/cells to each node.  For an all hexahedra mesh the ratio would be one to one.   For all prisms it would be 2 to 1.    And so on.   It looks like you have an all tet mesh which is small enough to have surface effects (which change the ratios).

Consider the grid attached in the figure below. The circles are representing the nodes and lines joining the two circles are representing elements. In the case attached, the number of nodes are 9 and number of elements are 12. Apply this on a large grid. The number of elements would be greater than number of nodes. 

You are free to call anything what you please.  But in the CFD program Fluent the 'elements' in the figure above are the squares and there are 4 of them.  This terminology (squares) would also be what 96% of FE methods would call the elements.    The exception being if this where a truss structure (for a bridge) and not a 2D partition of a fluid (the question posed).  And even then - they would usually be called 'beam elements' to make the exception clear.

Thanks a lot J. Blair Perot for pointing out the error. 

Ya  Mudassar

Fluent uses finite volume method where nodes stay at the center of the volume element.The example that you have provided has four elements with each element is having one node at the center. Now if you consider that circles are nodes, then there will be nine elemenets, one element for each node.

To J blair,

in the tetrahedral element also, node will remain at the center of element. are they remain at the corners?

thanks

vivek

Vivek,  you too, can call things whatever you like, but you would incorrect to think that is what Fluent calls them.  In Fluent the UNKNOWNS (for velocity, pressure, energy, etc) are indeed at the cell centers.   But cell centers are NOT called nodes. Cell centers are rashly called "cell centers" in Fluent.  Nodes are (in Fluent, and 95% of all other literature) the corners of the cells (vertices of the mesh).   Irrespective of what the cells look like.  

In classic low-order FE methods, the unknowns are often at the nodes (mesh vertices).  That does NOT mean that in FV methods the unknown locations are called nodes.  Nodes/vertices refer only to the mesh and are independent of any particular solution method.    There are node-based (dual mesh) FV methods (like CCM+) with the unknowns at the nodes.  And there are cell-based FV methods (like Fluent) with the unknowns at the cells.

And to give you a tiny hint.  A proper/decent/physically_correct CFD method has unknowns all over the place (cells, nodes, edges and faces).  Called staggered.  

In the 2D mesh below, you see

if the method is FD then there is no cell centroid. Unknowns are at the nodes or grids. 

If the method is FE then there is no cell centroid. Unknowns are at the nodes/ grids of the mesh elements.

If the method is FV, then cell centroid is there and unknowns are at the cell centroids. Using the spatial discretization method, those unknowns are projected at the nodes/grid points. 

I think this is clear.

thanks

vivek