Numerical Analysis of Nonlinear PDEs

Entropy decaying finite volume scheme for an aggregation-diffusion equation

Numerical Analysis of nonlinear PDEs is concerned with the construction and rigorous mathematical analysis of efficient, accurate and stable numerical algorithms for the approximate solution of partial differential equations.

Stimulated by ever-increasing demands from the natural sciences and engineering to provide reliable approximations to mathematical models involving nonlinear partial differential equations whose exact solutions are either too complicated to determine in closed form or, in many cases, are not known to exist, computational solution of PDEs has become a rich and active field of modern applied mathematics.

Specific areas of activity include:

- The construction and analysis of numerical algorithms (particularly finite element methods) for nonlinear PDEs in fluid mechanics (including the Navier-Stokes equations modelling the flow of viscous incompressible fluids, as well as kinetic models of dilute polymers and implicitly constituted fluid flow models for non-Newtonian flow problems);

- The development and analysis of numerical algorithms for nonlinear PDEs in solid mechanics, particularly free-discontinuity problems in fracture mechanics.

- Structure-preserving numerical schemes: finite volume schemes, particle methods and finite difference methods for gradient flows.

- Finite volume methods for balance laws: compressible fluid mechanics and related equations with applications in dynamic density functional theories and active particle models.

Faculty: José A. Carrillo and Endre Suli

Postdoctoral Fellows: Rafael Bailo

Students: Stefano Fronzoni, and Olav Haaland