Fondecyt project
Numerical Methods for Nonlinear Poroelasticity and Related Models with Applications in Biomedicine and Engineering
- Programme
- ANID, Fondecyt Postdoctoral Programme 2026
- Project
- N.º 3260398
- Principal investigator
- Cristian Inzunza
- Sponsoring researcher
- Sergio Caucao
- Start
- April 2026
Aims
The project develops and analyses mixed and mixed-primal finite element methods for nonlinear poroelasticity and related models, in which Biot's equations are coupled with nonlinear flow laws such as Brinkman and Forchheimer, and with transport or thermal effects.
- Variational formulations in Hilbert and Banach spaces, with proofs of existence, uniqueness and continuous dependence on the data.
- Discrete schemes that are stable and robust with respect to the physical parameters, in particular free of volumetric locking.
- A priori and a posteriori error estimates, and adaptive algorithms based on the latter.
- Numerical experiments motivated by applications in biomedicine and engineering.
Outputs 4
-
2026
A pseudostress-based fully mixed formulation for the unsteady Biot–Brinkman model
Preprint, GIANuC², Universidad Católica de la Santísima Concepción
-
2026
A pseudostress-based fully mixed finite element method for the stationary Biot–Poisson–Nernst–Planck system
Submitted
-
2026
Mixed finite element methods for a heat-assisted model of sedimentation
arXiv preprint arXiv:2610.28903
-
2026
A locking-free mixed-primal formulation for the Biot–Brinkman–Forchheimer model
Preprint 2026-9, GIANuC², Universidad Católica de la Santísima Concepción
Suggested acknowledgement
This work was supported by ANID–Chile through Fondecyt Postdoctorado project 3260398.