https://github.com/ucl/stokes-nc-ill-posed
Nonconforming ill posed stabilized fem for stokes problem
https://github.com/ucl/stokes-nc-ill-posed
Last synced: 25 days ago
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Nonconforming ill posed stabilized fem for stokes problem
- Host: GitHub
- URL: https://github.com/ucl/stokes-nc-ill-posed
- Owner: UCL
- License: mit
- Created: 2023-08-03T10:09:34.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2024-06-18T10:41:31.000Z (10 months ago)
- Last Synced: 2024-06-18T12:07:41.921Z (10 months ago)
- Language: Jupyter Notebook
- Size: 2.64 MB
- Stars: 1
- Watchers: 4
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# stokes-nc-ill-posed
Reproduction material for the paper
> Data assimilation nonconforming finite element methods for transient Stokes problem
>
> * authors: Erik Burman, Deepika Garg and Janosch Preuss
> * University College London
The numerical experiments have been implemented using the Software [ngsolve](https://ngsolve.org/).
More precisely we used the software at commit `a8b62a566f421f3e7942ed95e7cdc586e326b33c` related to [this](https://github.com/NGSolve/ngsolve) github repository.
The reproduction files are available in terms of `jupyter` notebooks in the folder `ngsolve`.
## Section 5.1. Convergence Study: Stokes problem
### Fig.2
The notebook to reproduce these results is `Stokes-non-conforming-clean-data.ipynb`.
In the second cell of the notebook the discretization parameters have to be set.
To reproduce the results in the figure the notebook should be run consecutively with the following parameters:
```
N = 1
hmax = 0.6
N = 2
hmax = 0.3
N = 4
hmax = 0.15
N = 8
hmax = 0.075
N = 16
hmax = 0.0375
```
The corresponding errors are printed when running the notebook. The quantities of interest (shown in the Fig.2) are
```
L2 error velocity at time step 0 = ...
L2 error velocity at time step N = ...
L2 error pressure at time step N = ...
delta norm = ...
```
### Fig.3
The notebook to reproduce these results is `Stokes-non-conforming_const_noise.ipynb`.
### Fig.3 (a)
To reproduce these results we have to fix the parameters
```
N = 16
hamx = 0.0375
```
in the second cell of the notebook. The parameter which has to be varied from 1e-5 to 1e1 is called `constant_noise_data` (it is also in the second cell of the notebook). We run the notebook consecutively changing this parameter and monitor the results. The output shown in the figure is
```
l2_err at t = [0,T/8,T/4,T/2,T] = ...
delta norm = ...
```
### Fig.3 (b)
To reproduce these results we have to fix `constant_noise_data = 2e-1` and run the script repreatedly with the following discretization parameters:
```
N = 1
hmax = 0.6
N = 2
hmax = 0.3
N = 4
hmax = 0.15
N = 8
hmax = 0.075
N = 16
hmax = 0.0375
```
## Section 5.2. Navier-Stokes equations
### Fig. 4
The notebook to reproduce these results is `Navier-Stokes.ipynb`. The parameters to be changed are in the second cell of the notebook. Run the notebook repeatedly with the follwing discretization parameters:
```
N = 2
hmax = 0.4
N = 4
hmax = 0.2
N = 8
hmax = 0.1
N = 12
hmax = 0.075
N = 16
hmax = 0.05
```
Note that a fixed point iteration is run and in each iteration step the errors
```
L2-error velocity final time: ...
L2-error pressure final time: ...
L2-error velocity initial time: ...
epsilon norm = ...
```
The values shown in the Fig.4 are taken from the final step of the fixed point iteration.