On 5/21/21 7:37 PM, 沈键 wrote:
Thanks for your reply, sir. I'm new to FEM and for some concepts, I don't have
clear understanding. I still have some problems：
> Then you would want to compute the projection of d/dx u_h into this space via
(phi_i, grad_x) = (phi_i, d/dx u_h)
-------------------------------------
Is u_h means finite element method solution? If I'm right, how to understand
`(phi_i, grad_x) = (phi_i, d/dx u_h)`? Why they are
equal?
Yes, u_h is the solution for which you want to output the gradient.
I should have chosen a different name than grad_x. I didn't mean this to be
the gradient operator, but a function that corresponds to d/dx u_h. Let me
call this function gx, then you want to solve the problem
(phi_i, gx) = (phi_i, d/dx u_h) for all shape functions phi_i
and similarly if you want to output a continuous version of d/dy u_h, you'd
solve for a function gy that satisfies
(phi_i, gy) = (phi_i, d/dy u_h) for all shape functions phi_i
If you expand gx as
gx(x) = \sum_j GX_j phi_j(x)
then the problem you are trying to solve is
(phi_i, gx)
= \sum_j (phi_i,phi_j) GX_j
= (phi_i, d/dx u_h)
where M_ij = (phi_i,phi_j) is the mass matrix.
Best
W.
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Wolfgang Bangerth email: [email protected]
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