Help with Bending Domain and Locking

Hi all,

I have a general question. I know that one of the ways to avoid locking is to use higher order meshes. Suppose I have created a mesh in GMSH and set its order to be 2. Now my question is do I have to also define a quadratic vector function space on this mesh or a linear vector function space will do?
I am asking this question because my mesh is already big and having both the mesh and the function space defined as quadratic causes even our super computer to run out of memory.

Thank you in advance.