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The virtual element method and its applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	The virtual element method and its applicationsedited by Paola F. Antonietti, Lourenco Beirao da Veiga, Gianmarco Manzini.
other author:	Antonietti, Paola F.
Published:	Cham :Springer International Publishing :2022.
Description:	xxiv, 605 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Numerical analysis.
Online resource:	https://doi.org/10.1007/978-3-030-95319-5
ISBN:	9783030953195$q(electronic bk.)

The virtual element method and its applications
The virtual element method and its applications[electronic resource] /edited by Paola F. Antonietti, Lourenco Beirao da Veiga, Gianmarco Manzini. - Cham :Springer International Publishing :2022. - xxiv, 605 p. :ill., digital ;24 cm. - SEMA SIMAI Springer series,v. 312199-305X ;. - SEMA SIMAI Springer series ;v.4..

1 Tommaso Sorgente et al., VEM and the Mesh -- 2 Dibyendu Adak et al., On the implementation of Virtual Element Method for Nonlinear problems over polygonal meshes -- 3 Long Chen and Xuehai Huang, Discrete Hessian Complexes in Three Dimensions -- 4 Edoardo Artioli et al., Some Virtual Element Methods for Infinitesimal Elasticity Problems -- 5 Lourenço Beirão da Veiga and Giuseppe Vacca, An introduction to second order divergence-free VEM for fluidodynamics -- 6 Gabriel N. Gatica et al, A virtual marriage à la mode: some recent results on the coupling of VEM and BEM -- 7 Daniele Boffi et al., Virtual element approximation of eigenvalue problems -- 8 David Mora and Alberth Silgado, Virtual element methods for a stream-function formulation of the Oseen equations -- 9 Lorenzo Mascotto et al., The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation -- 10 Paola F. Antonietti et al., The conforming virtual element method for polyharmonic and elastodynamics problems: a review -- 11 Edoardo Artioli et al., The virtual element method in nonlinear and fracture solid mechanics -- 12 Sebastián Naranjo Álvarez et al., The virtual element method for the coupled system of magneto-hydrodynamics -- 13 Peter Wriggers et al., Virtual Element Methods for Engineering Applications.

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.

ISBN: 9783030953195$q(electronic bk.)

Standard No.: 10.1007/978-3-030-95319-5doiSubjects--Topical Terms:

182073
Numerical analysis.

LC Class. No.: QA297 / .V57 2022

Dewey Class. No.: 518

The virtual element method and its applications
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505 0 $a 1 Tommaso Sorgente et al., VEM and the Mesh -- 2 Dibyendu Adak et al., On the implementation of Virtual Element Method for Nonlinear problems over polygonal meshes -- 3 Long Chen and Xuehai Huang, Discrete Hessian Complexes in Three Dimensions -- 4 Edoardo Artioli et al., Some Virtual Element Methods for Infinitesimal Elasticity Problems -- 5 Lourenço Beirão da Veiga and Giuseppe Vacca, An introduction to second order divergence-free VEM for fluidodynamics -- 6 Gabriel N. Gatica et al, A virtual marriage à la mode: some recent results on the coupling of VEM and BEM -- 7 Daniele Boffi et al., Virtual element approximation of eigenvalue problems -- 8 David Mora and Alberth Silgado, Virtual element methods for a stream-function formulation of the Oseen equations -- 9 Lorenzo Mascotto et al., The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation -- 10 Paola F. Antonietti et al., The conforming virtual element method for polyharmonic and elastodynamics problems: a review -- 11 Edoardo Artioli et al., The virtual element method in nonlinear and fracture solid mechanics -- 12 Sebastián Naranjo Álvarez et al., The virtual element method for the coupled system of magneto-hydrodynamics -- 13 Peter Wriggers et al., Virtual Element Methods for Engineering Applications.
520 $a 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.
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650 2 4 $a Applications of Mathematics. $3 273744
700 1 $a Antonietti, Paola F. $3 937290
700 1 $a Beirao da Veiga, Lourenco. $3 937291
700 1 $a Manzini, Gianmarco. $3 681712
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950 $a Mathematics and Statistics (SpringerNature-11649)