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Hybrid high-order methods. A primer with application to solid mechanics
arXiv - CS - Numerical Analysis Pub Date : 2021-06-17 , DOI: arxiv-2106.09348
Matteo Cicuttin, Alexandre Ern, Nicolas Pignet

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.

中文翻译:

混合高阶方法。适用于固体力学的入门读物

本书分为八章。前三个简单地介绍了线性扩散问题的混合高阶方法的基本原理、数学分析背后的关键思想、该方法的一些有用变体以及与文献中其他方法的链接。以下四个介绍了固体力学的各种具有挑战性的应用,包括线性弹性和超弹性、弹性动力学、接触/摩擦和塑性。最后一章回顾了实施方面。本书主要面向研究生、研究人员(应用数学、数值分析和计算力学)和在相关应用领域工作的工程师。假定具有有限元方法的设计和分析的基本知识。
更新日期:2021-06-18
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