The Virtual Element Method and its Applications

The Virtual Element Method (VEM) is a numerical technique for solving partial differential equations (PDEs). This book presents the current state of the art of VEM, covering theoretical and computational aspects, as well as challenging applications in computational mechanics, fluid dynamics, and wave propagation phenomena. It is intended for graduate students and researchers in mathematics and engineering fields.

Format: Hardback
Length: 605 pages
Publication date: 09 October 2022
Publisher: Springer Nature Switzerland AG

The Virtual Element Method (VEM) is a cutting-edge numerical technique that has gained significant attention in recent years. Its purpose is to provide a comprehensive overview of the current state-of-the-art in this field, by gathering contributions from numerous prominent researchers. This book aims to cover a wide range of topics, ranging from the mathematical foundations of VEM to its practical computational applications.

The book is organized into three distinct parts. The first part focuses on recent advancements in theoretical and computational aspects of VEMs. It discusses the generality of meshes suitable for VEM, the implementation of VEM for linear and nonlinear partial differential equations (PDEs), and the construction of discrete hessian complexes. This section provides a solid foundation for understanding the theoretical principles and computational techniques associated with VEM.

The second part of the volume delves into the Virtual Element discretization of paradigmatic linear and non-linear partial differential problems from computational mechanics, fluid dynamics, and wave propagation phenomena. It explores the application of VEM to solve complex problems in these fields, such as the modeling of materials with fractures, magneto-hydrodynamics phenomena, and contact solid mechanics. This part showcases the versatility and effectiveness of VEM in addressing real-world problems.

The third part of the book presents challenging applications such as the modeling of materials with fractures, magneto-hydrodynamics phenomena, and contact solid mechanics. It discusses the theoretical background and computational methodologies employed to solve these problems, providing valuable insights into the latest developments in the field.

This book is designed primarily for graduate students and researchers in mathematics and engineering fields who are interested in learning novel numerical techniques for the solution of partial differential equations. It serves as a valuable reference material for numerical analysts and practitioners in the field.

In conclusion, the Virtual Element Method (VEM) has emerged as a powerful tool for solving complex partial differential equations. This book provides a comprehensive and up-to-date overview of the current state-of-the-art in VEM, covering a wide range of topics and presenting challenging applications. It is an essential resource for graduate students, researchers, and practitioners in mathematics and engineering fields who are interested in advancing their knowledge in this field.

Weight: 1105g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030953188
Edition number: 1st ed. 2022