Applied and Computational Partial Differential Equations

Partial differential equations (PDEs) are often the elective tools for the modelization of complex phenomena. The research activity of our groups covers a whole spectrum of themes in Applied and Computational PDEs, encompassing modeling, analysis, numerics, and computations. In particular, we work on:

Computational, analytical, and data-driven techniques to tackle problems in cosmology and astrophysics, focusing on the equations and simulation methods related to studying the formation of cosmic structure, with the ultimate aim to confront theory and observations and understand better the mysteries of our Universe;

The design, implementation and numerical analysis of adaptive, data-driven computational methods based on low-rank tensor approximation, primarily aimed at the efficient numerical solution of PDEs by using vast, generic parameter spaces, which are computationally infeasible for classical approaches;

Emergent phenomena in biology, medicine and social sciences by systematically deriving, analysing and simulating PDE-based models. A particular focus is problems in cell biology and collective dynamics, where we work with experimentalists and their data. Our methods include tools from kinetic theory and probability theory;

Finite element methods for partial differential equations, focusing on the design, numerical analysis, and efficient implementation of advanced discretization techniques, with applications to elliptic, wave propagation, and nonlinear reaction–diffusion problems;

Variational evolution problems, their analysis and approximation, with application to the description of the behavior of continuum and discrete systems, optimal shapes and structures, and multiphysics effects in solids.

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