# Degree of freedom for elastic wave propagation problem

I am solving a elastodynamics (vector valued elastic wave) equation.

I create the 2D mesh in Gmsh discretised into triangular elements of second order. Therefore, it is my understanding that the element is a triangle with total six nodes, i.e., 3 vertices and 1 node on each of the 3 edges. I have the following questions:

Q.1: The dof for a simple scalar problem is equal to the no. of nodes on the mesh. Therefore, the dof for my problem should be equal to twice the no. of nodes on the mesh right? This is because each node can only experience displacement in 'x' or 'y' direction as a result of wave propagation. Is this correct?

Q.2: Each triangular element on the mesh will have 12 dof. Right?

I read somewhere that the velocity of wave in both directions will also constitute 2 dof, but that doesn't seem to make sense.

• Q1: yes. Q2: yes. Other element formulations are possible but the one you have described is by far the most common. Jan 8, 2017 at 21:59
• As pointed out by @BillGreene, while not common, there can be non-standard formulations. Assuming it's a possible formulation, if your unknown is a scalar potential and the vector (of displacement) is derived as a gradient of the potential, then you are back to 6 dofs. It is best to write down your equation / formulation in order to count your unknowns. Don't count your dofs before the equations are hatched :-) Jan 9, 2017 at 1:56
• @NameRakes Thanks! In this case I am referring to the standard elastic wave equation used for simulating seismic wave. Is the assessment correct in this case then?
– CRG
Jan 9, 2017 at 2:47