$L^2$ Projection

mathematics
1

Hello dear all,

I have question about L^2 projection in fenics… specifically if I have solution vector u to pde, I can get gradients by using commands

V_vec = VectorFunctionSpace(mesh, "CG",1)
gradu = project(grad(u),V_vec)

however, I have a doubt… when we make ‘grad(u)’, what function space does ‘grad(u)’ live in? Why is necessary to project onto space given by ‘V_vec = VectorFunctionSpace(mesh, “CG”,1)’?

Thank you…
Bhagat

2

That’s what the second argument says: V_vec.

If u is a scalar, is necessary the V_vec is a space of vectors. Apart from that, it’s up to you to choose "CG", 1, or any other space which you may deem appropriate.

3

Thank you for your reply… I meant something slightly different. If I say for example

gu = grad(u)

and I look at object ‘gu’ before calling project function, what function space does ‘gu’ live in before projection?

Also CG means continuous galerkin yes?

4

or said differently… what exactly is the object ‘grad(u)’?

5

It’s a ufl object, which does not belong to any function space.

1 Like
6

ok… thank you very much sir.