Cristian Inzunza
Mixed finite element methods for nonlinear and coupled PDEs, with a focus on poroelasticity, flow in porous media and transport.
About me
Since November 2026 I have been a full-time faculty member in the Department of Mathematics, Faculty of Sciences, Universidad de La Serena, Chile. I am also the principal investigator of the ANID Fondecyt Postdoctoral project No. 3260398, Numerical Methods for Nonlinear Poroelasticity and Related Models with Applications in Biomedicine and Engineering, which I started in April 2026 under the sponsorship of Prof. Sergio Caucao, and a member of the Numerical Analysis and Scientific Computing Research Group (GIANuC²).
From April 2025 to March 2026 I was a postdoctoral researcher at the Center for Mathematical Modeling (CMM), Universidad de Chile, working on finite element methods for nonlinear problems with biomedical and engineering applications, under the supervision of Prof. Sergio Caucao and Prof. Jessika Camaño.
I received my Ph.D. in Applied Sciences with a mention in Mathematical Engineering from the Universidad de Concepción (2020–2024), advised by Prof. Gabriel N. Gatica, after earning my degree in Mathematical Civil Engineering at the same university (2011–2018).
I work on the numerical analysis of nonlinear and coupled partial differential equations, mainly through mixed finite element methods in Banach spaces. The models come from continuum mechanics: poroelasticity, heat transfer, stress-assisted diffusion and chemotaxis–fluid interaction. Their multiphysics coupling leads to nonstandard variational formulations, whose well-posedness, discrete stability and error analysis are the core of my work.
Research
- Poroelasticity and multiphysics coupling Biot's consolidation model coupled with heat transfer, electrochemical transport and fluid inertia.
- Flow in porous media and incompressible fluids Mixed methods for Stokes, Navier–Stokes, Brinkman and Brinkman–Forchheimer flows.
- Transport, diffusion and their coupling with mechanics Stress-assisted diffusion, chemotaxis–fluid interaction, Boussinesq flows and sedimentation.
- A posteriori error analysis and adaptivity Reliable and efficient residual estimators for mixed methods in Banach spaces.
News
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Joined the Department of Mathematics, Universidad de La Serena, as a full-time faculty member.
Recent articles
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2027
A priori and a posteriori error analysis of a mixed FEM for stationary convective Brinkman–Forchheimer flows with variable porosity
Journal of Computational and Applied Mathematics, 492, Article 118115
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2026
A five-field mixed formulation for the fully dynamic Biot–Brinkman model
ESAIM: Mathematical Modelling and Numerical Analysis, accepted
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2025
Primal-mixed finite element methods for the coupled Biot and Poisson–Nernst–Planck equations
Computers & Mathematics with Applications, 186, 53–83