• Franco Dassi, University Milano Bicocca
• André Harnist
• Xin Liu
• Ilario Mazzieri

In the last decades, computational methods for the resolution of Partial Differential Equations (PDEs) over polytopal meshes attracted the interests of a large number of researchers and engineers. The most evident advantage of such methods involves a better flexibility in the discretization of the computational domain. Indeed, they allow the presence of hanging nodes, non-convex cells, and non-matching interfaces in the computational domain without any "ad-hoc" procedure to deal with each of these arbitrary configurations.

However, there is a more hidden and sophisticated advantage: the flexibility in defining discrete spaces makes possible to obtain discrete functions characterized by very useful properties. In recent years this aspect has been fully exploited to obtain advantages on the numerical solution itself. For example, it was used to get a divergence-free numerical approximation of Stokes or Navier-Stokes problems.

The goal on this mini-simposium is to discuss the recent findings and developments of polytopal numerical schemes including Discontinuos Galerkin (DG), Hybrid High-Order (HHO), and Virtual Element (VE) methods. The topics include (but are not limited to) the following aspects: i) resolution of fluid dynamics, mechanics, or electromagnetism PDEs; ii) h-, p-, hp-adaptivity; iii) challenges in code development on modern architectures.

We plan to organize the mini-symposium into 2 sessions. We will decide the session formats, 1 keynote plus 4 invited contributions or 6 invited contributions, according to the speakers' answers to our invitations.

Keywords: Numerical methods, Partial differential equations, Polygonal and polyhedral meshes.