2025/03/01 by Daniele A. Di Pietro, Jérôme Droniou, Di Pietro, Daniele A. +1 · 2 citations
Engineering · #65N12 #65N30 #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2503.00425
openalex publication_date 2025/03/01 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
This document contains lecture notes from the Ph.D. course given at Scuola Superiore Meridionale by Daniele Di Pietro in February 2025. The goal of the course is to provide an overview of polytopal methods, focusing on the Hybrid High-Order (HHO) method. As a starting point, we study the Crouzeix-Raviart method for a pure diffusion equation, with particular focus on its stability. We then show that, switching to a fully discrete point of view, it is possible to generalize it first to polyhedral meshes and then to arbitrary order, leading to a method that belongs to the HHO family. A study of the stability and consistency of this method reveals the need for a stabilization term, for which we identify two key properties.