Supplementary material for "Spurious oscillations in the numerical approximations of poroelasticity problems: Diffusion and saddle-point sources"

This set contains Jupyter notebooks with the numerical tests performed for the paper "Spurious oscillations in the numerical approximations of poroelasticity problems: Diffusion and saddle-point sources".

Ferreira, C. A. S., Honório, H. T., Nick, H. M., Maliska, C. R. 2026. Spurious oscillations in the numerical approximations of poroelasticity problems: Diffusion and saddle-point sources. Computer and Mathematics with Applications. https://doi.org/10.1016/j.camwa.2026.04.021

The Jupyter notebooks in this set are as follows:
- convergence_analysis.ipynb:convergence_analysis.ipynb: This notebook is associated with Figure 1 of the paper and validates all the numerical methods discussed in the main paper against analytical solutions. It also shows the convergence of the methods.
- diffusion_oscillations_test.ipynb: This notebook is associated with Figure 2 of the paper and illustrates the occurrence of diffusion oscillations by comparing the numerical solution of diffusion-like problems using cell-center finite volume and P1 finite element approximations. It also considers a stabilization technique (referred to as FPL-stabilization) for the P1 finite element case.
- saddle_point_oscillations_test_1.ipynb: This notebook is associated with Figure 3 of the paper and discerns the occurrence of diffusion and saddle-point problems, along with the dependence of the latter with the stiffness contrast between drained and undrained response.
- saddle_point_oscillations_test_2.ipynb: This notebook is associated with Figure 4 of the paper and demonstrates the effectiveness of different stabilization techniques for consolidation problems solved using finite element approximations.
- saddle_point_oscillations_test_3.ipynb: This notebook is associated with Figure 5 of the paper and demonstrates the effectiveness of different stabilization techniques for consolidation problems solved using finite volume approximations.

This set also includes a JSON file containing poroelastic properties for different porous media obtained from Cheng (2016).

Cheng, A. H.-D. 2016. Poroelasticity. Volume 27. Springer. https://doi.org/10.1007/978-3-319-25202-5

If you use this dataset in your work, include these citations:

Ferreira, C. A. S., Honório, H. T., Nick, H. M., Maliska, C. R. 2026. Spurious oscillations in the numerical approximations of poroelasticity problems: Diffusion and saddle-point sources. Computer and Mathematics with Applications. https://doi.org/10.1016/j.camwa.2026.04.021

Ferreira, C. A. S. 2026. Supplementary material for "Spurious oscillations in the numerical approximations of poroelasticity problems: Diffusion and saddle-point sources". DTU Data. https://doi.org/10.11583/DTU.28194449