The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

Many real-world problems involve fluids in motion. The goal of this book is to propose a new
approach to numerical analysis of the underlying nonlinear equations in the spirit of the …

We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …

Two discrete functional analysis tools are established for spaces of piecewise polynomial
functions on general meshes:(i) a discrete counterpart of the continuous Sobolev …

In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady
nonlinear Leray–Lions problems. The proposed method has several assets, including the …

Mathematical models of protein–protein dynamics, such as the heterodimer model, play a
crucial role in understanding many physical phenomena, eg, the progression of some …

We prove several discrete Gagliardo–Nirenberg–Sobolev and Poincaré–Sobolev
inequalities for some approximations with arbitrary boundary values on finite volume …

The paper is concerned with the construction and convergence analysis of a discontinuous
Galerkin finite element method for the Cahn–Hilliard equation with convection. Using …