Hybrid high-order methods for interface problems

The purpose of this Ph.D. thesis is to design and analyze Hybrid High-Order (HHO) methods on some interface problems. By interface, we mean (i) diffuse interface, and (ii) interface as an immersed boundary. The first half of this manuscript is dedicated to diffuse interfaces, more precisely we consider the so called Cahn–Hilliard problem that models the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. In the second half, we deal with the interface as an immersed boundary and consider a hybrid dimensional model for the simulation of Darcy flows and passive transport in fractured porous media, in which the fracture is considered as an hyperplane that crosses our domain of interest.

metodo ibrido di alto ordine per problemi di interfaccia