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Hypercircle method for the poseriori and the priori error estimation for Poisson's equation with discontinuous coefficients.
Basic settings
Xuefeng LIU (2024)
The problems for computation are limited to the ones on a square domain with four sub-domains:
$$
\Omega = \Omega_1 \cup \Omega_2 \cup \Omega_3 \cup \Omega_4,
$$
where
$$
\Omega_1 = [0,1)^2;~~
\Omega_2 = (-1,0]\times [0,1);~~
\Omega_3 = (-1,0]^2;~~
\Omega_4 = [0,1)\times (-1,0].
$$
The setting of problem is located in case folders. For example, in "case_1", the following setting is defined in "problem_setting.py":
alpha = 0.535440945602466
alpha_list = [5,1,5,1]
Coeff_A = [0.447213595499958,-0.745355992499875, -0.944117590499871,-2.401702642499717]
Coeff_B = [1.0, 2.333333333333333, 0.555555555555567, -0.481481481481390]
Step by step instruction
- Step 1: For each computation case, configure the "problem_setting.py" in the case folder.
- Step 2: Set the value of subdivision number N and then run all the cells in
Hypercircle.ipynb.
Note: To run a different case, please clear the kernel of the notebook.
Cases
- Case 1:
alpha = 0.535440945602466; alpha_list = [5,1,5,1] - Case 2:
alpha = 1; alpha_list = [5,1,1,5] - Case 3:
alpha = 0.126902069722214; alpha_list = [100,1,100,1]
About the directory
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