During our finite element course, we've solved the linear elasticity problem in 2D on a square (GridGenerator::hyper_cube) with $Q_1$ bilinear finite elements in each component. We imposed neumann homogeneous boundary conditions on one face, and homogeneous Dirichlet on the other three faces.

As outputs, we chose:

  • magnitude of the solution $u$
  • $u_x$ (x-displacement)
  • $u_y$ (y-displacement)

The output of the magnitude of $u$ is the following: enter image description here

So far so good. Now, I select $u_x$, and I'd like to warp it by scalar, as it is a scalar valued function. So first let's see $u_x$: enter image description here

Now, I warp this $u_x$ by scalar, and the plot is the following:

enter image description here

i.e. it seems that the solution is flat, which is absolutely non-sense. Also, if I increase the scale factor, I got something which to me doesn't make any sense at all:

enter image description here

Does anyone know if this is normal, or is there something wrong in my finite element solver? If the latter, this would really surprise me

  • $\begingroup$ What is the boundary condition? $\endgroup$
    – knl
    Commented Jun 28, 2021 at 18:42
  • $\begingroup$ Neumann homogeneous everywhere, except on the left boundary, where is homogeneous Dirichlet. @knl $\endgroup$
    – FEGirl
    Commented Jun 28, 2021 at 18:44
  • 1
    $\begingroup$ Where is the loading coming from? $\endgroup$
    – knl
    Commented Jun 28, 2021 at 18:56
  • 1
    $\begingroup$ $u$ is a vector, so $\nabla u$ is a 2-tensor and $\mathrm{div}(C\nabla u)$ is again a vector. What do you mean by "vector equals -1"? $\endgroup$
    – knl
    Commented Jun 29, 2021 at 14:42
  • 5
    $\begingroup$ Which quantity do you warp by? "Warp by scalar" just means that you choose one scalar field to provide a third dimension to the plot, but there are many quantities that one could choose: The x-displacement itself, the magnitude of the displacement, the size of cells, the distortion of cells, etc. $\endgroup$ Commented Jun 29, 2021 at 15:52

1 Answer 1


It seems like you are using deal-ii for your simulations. Its a well established fem solver and there is a very less chance that the mistake is with the FEM solver. However, Please check the BC that you have applied to your problem ( In case, if above is not the expected solution )

Try scaling up the data using calculator filter in Paraview and then try “warp by scalar” filter on top of that to verify the plots

  • $\begingroup$ I agree with you for the FEM solver part. As you can see, my BCs are fulfilled: I required neumann homogeneous everywhere, except on the left face, where I have homogeneous Dirichlet. I think the problems comes from the fact that the scalars that I was using to "warp" were the ones from the estimator, which is one output of my fem solver. $\endgroup$
    – FEGirl
    Commented Jun 28, 2021 at 20:22
  • 1
    $\begingroup$ Please be clear on what you need to ask on the forum , if you find any obervations, edit the posted question immediately. $\endgroup$ Commented Jun 29, 2021 at 20:05

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