Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains

This book develops graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains, focusing on second-order equations with constant coefficients. It is written for mathematics graduate students and researchers, but is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods.

Format: Paperback / softback
Length: 179 pages
Publication date: 03 September 2022
Publisher: Springer International Publishing AG

This book presents a comprehensive and innovative approach to solving singular elliptic boundary value problems in two- and three-dimensional domains. By employing a class of graded finite element methods, it offers a systematic framework for addressing these complex mathematical challenges. The author's clear and concise presentation encompasses both the mathematical theory and the numerical tools required to effectively handle the intricate aspects of singular solutions.

Furthermore, by concentrating on second-order equations with constant coefficients, the book achieves the remarkable feat of deriving explicit results that are accessible to a broader audience, including applied and computational mathematicians, scientists, and engineers involved in numerical methods. While primarily designed for mathematics graduate students and researchers, this book also holds significant relevance to applied and computational mathematicians, scientists, and engineers who may encounter singular problems in their work.

The book begins by introducing the fundamental concepts and theoretical foundations of singular elliptic boundary value problems. It then delves into the development of graded finite element methods, highlighting their advantages and limitations. The author provides detailed explanations of the underlying mathematical principles, including the theory of elliptic equations, the concept of boundary elements, and the theory of finite elements.

Throughout the book, practical examples and case studies are employed to illustrate the theoretical concepts and demonstrate the effectiveness of the proposed methods. These examples cover a wide range of applications, including fluid dynamics, solid mechanics, and heat transfer, making the material accessible to a diverse audience. The book also includes a comprehensive bibliography that provides further reading for those interested in exploring the topic in greater depth.

In conclusion, this book is a valuable resource for anyone seeking to advance their understanding of singular elliptic boundary value problems. Its comprehensive presentation, coupled with practical examples and detailed explanations, makes it an essential tool for both researchers and practitioners in the field. By providing a solid foundation in mathematical theory and numerical techniques, this book enables readers to tackle complex singular problems with confidence and efficiency.

Weight: 302g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031058202
Edition number: 1st ed. 2022