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;

Asymptotical, theoretical, and numerical analysis of atmospheric flow models for cloudy air towards deriving reduced models for particular weather phenomena based on scale analysis and studying the global well posedness of the models;

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;
 
Kinetic theory applied to the study of emergent phenomena in biology, medicine and social sciences by coupling PDEs with probability theory and developing modeling and simulations;

Finite element methods for the numerical approximation of PDEs, focusing on the design and the analysis of standard and non standard finite element methods (discontinuous Galerkin methods, virtual
element methods, finite elements with operator-adapted basis functions, space-time methods, reduced basis methods) for elliptic, parabolic, and wave propagation 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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