Hybrid high-order methods. A primer with application to solid mechanics

TL;DR

This book provides a comprehensive introduction to hybrid high-order methods, covering their mathematical foundations and diverse applications in solid mechanics, aimed at graduate students and researchers in numerical analysis and engineering.

Contribution

It offers a clear, streamlined presentation of hybrid high-order methods, including their principles, variants, and applications to complex solid mechanics problems.

Findings

Effective application to linear elasticity and hyperelasticity

Insights into elastodynamics, contact, and plasticity modeling

Implementation guidance for practical use

Abstract

This book is organized into eight chapters. The first three gently introduce the basic principles of hybrid high-order methods on a linear diffusion problem, the key ideas underlying the mathematical analysis, and some useful variants of the method as well as links to other methods from the literature. The following four present various challenging applications to solid mechanics, including linear elasticity and hyperelasticity, elastodynamics, contact/friction, and plasticity. The last chapter reviews implementation aspects. This book is primarily intended for graduate students, researchers (in applied mathematics, numerical analysis, and computational mechanics), and engineers working in related fields of application. Basic knowledge of the devising and analysis of finite element methods is assumed. Special effort was made to streamline the presentation so as to pinpoint the essential ideas, address key mathematical aspects, present examples, and provide bibliographic pointers.