Convergence issues faced in strain L2 function

[Pratyusa Kar]

Hi, 

I have a simple 2D linear elasticity problem, a square domain x(0,1), y(0,1). In that I am fixing x=0 in all directions and applying a displacement of 0.02 along x direction at the edge x=1.

I am facing issues with the strain L2 function convergence in my code. Couple of checks I already did:

- The main solver and field calculation runs fine. Gives meaningful plot of u which shows boundary conditions are fine. 

- In the compute strain projection function, I printed strain_xx_cell_rhs(i) (which prints ux,0 )

- I also printed cell_matrix. 

The code does not converge with the CG solver. Since the problem is simple, I am not sure if I am missing something. Any help will be appreciated. 

I have attached the main.cc and a snapshot of the error.

Thank you. 

[Pratyusa Kar]

Also I checked with a 4 element mesh and 1 quadrature point. However, I see a noninvertible mass matrix. I do not understand what is missing in the code. 

Thank you. 

[Wolfgang Bangerth]

On 12/15/24 08:40, Pratyusa Kar wrote:
> Also I checked with a 4 element mesh and 1 quadrature point. However, I see a
> noninvertible mass matrix. I do not understand what is missing in the code.

Pratyusa:
OK, so you already determined that the matrix is not invertible. The question
is why. What happens if you have only one cell? Or you look at the cell matrix
of a single cell?

I don't understand what you mean by "and 1 quadrature point". I checked with
your code, and if I understand correctly, you are using a Q1 element to
project the strain onto, and that you are using a 2x2 Gauss formula. That
seems appropriate.

I looked at your code, and I do not understand why fe_L2 is vector valued. You
are trying to project individual components of the strain onto a finite
element. The individual components are scalars. Why is fe_L2 not also a scalar?

Best
W.

--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Pratyusa Kar]

Hi Dr. Bangerth,

Thank you for the explanation. 

Yes I just did the problem with 1 element and figured out that because I was using vector to output the strain the errors come up. I should have checked this before. 

Now with scalar definition my problem is converging even with multiple elements and proper refined mesh. 

 Thank you. 

Regards,

Pratyusa

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