The Virtual Element Method and its Applications
Buch in deiner Nähe kaufen
Beschreibung
The purpose of this book is to present the current state of the art of the Virtual Element Method (VEM) by collecting contributions from many of the most active researchers in this field and covering a broad range of topics: from the mathematical foundation to real life computational applications.
The book is naturally divided into three parts. The first part of the book presents recent advances in theoretical and computational aspects of VEMs, discussing the generality of the meshes suitable to the VEM, the implementation of the VEM for linear and nonlinear PDEs, and the construction of discrete hessian complexes. The second part of the volume discusses Virtual Element discretization of paradigmatic linear and non-linear partial differential problems from computational mechanics, fluid dynamics, and wave propagation phenomena. Finally, the third part contains challenging applications such as the modeling of materials with fractures, magneto-hydrodynamics phenomena and contact solid mechanics.
The book is intended for graduate students and researchers in mathematics and engineering fields, interested in learning novel numerical techniques for the solution of partial differential equations. It may as well serve as useful reference material for numerical analysts practitioners of the field.
The purpose of this book is to present the current state of the art of the Virtual Element Method (VEM) by collecting contributions from many of the most active researchers in this field and covering a broad range of topics: from the mathematical foundation to real life computational applications.
The book is naturally divided into three parts. The first part of the book presents recent advances in theoretical and computational aspects of VEMs, discussing the generality of the meshes suitable to the VEM, the implementation of the VEM for linear and nonlinear PDEs, and the construction of discrete hessian complexes. The second part of the volume discusses Virtual Element discretization of paradigmatic linear and non-linear partial differential problems from computational mechanics, fluid dynamics, and wave propagation phenomena. Finally, the third part contains challenging applications such as the modeling of materials with fractures, magneto-hydrodynamics phenomena and contact solid mechanics.
The book is intended for graduate students and researchers in mathematics and engineering fields, interested in learning novel numerical techniques for the solution of partial differential equations. It may as well serve as useful reference material for numerical analysts practitioners of the field.
Provides a comprehensive review of the rapidly expanding field of the virtual element methods Includes in-depth discussions on the design and analysis of the virtual element method Covers a vast array of special topics and applications illustrating the wide use of the virtual element method
Autor*in
Paola F. Antonietti
Themen in »The Virtual Element Method and its Applications«
Virtual Element Method Galerkin Methods Polygonal and Polytopal Meshes Linear and Nonlinear Partial Differential Equations Discrete Hessian Complexes in Three Dimensions Elasticity Divergence-free Methods for Fluidodynamics Boundary Element Methods Eigenvalue Problems Oseen Equation Helmholtz Equation Polyharmonic Problems Nonlinear and Fracture Solid Mechanics Magneto-Hydrodynamics Fractured Materials