Title Statements
- Full title :The Virtual Element Method and Its Applications.
Edition Statements
- Publication Date:©2022.
Publication Statements
- Publisher(s):Springer International Publishing AG
- Place of Publication:Cham
- Language:eng
- Publication Date:©2022.
Notes
11.3 Basis of the VEM in 2D Solid Mechanics.
The Physical Object
- Description:1 online resource (621 pages).
Edition Identifiers
- ISBN:9783030953195, 303095319X
- oclc:on1349953523
- LC Classification:QA299.6-433
Table of Contents
Intro -- Preface -- Contents -- Editors and Contributors -- About the Editors -- Contributors -- 1 VEM and the Mesh -- 1.1 Introduction -- 1.2 Model Problem -- 1.3 State of the Art -- 1.3.1 Geometrical Assumptions -- 1.3.2 Convergence Results in the VEM Literature -- 1.4 Violating the Geometrical Assumptions -- 1.4.1 Datasets Definition -- 1.4.2 VEM Performance over the Datasets -- 1.5 Mesh Quality Metrics -- 1.5.1 Polygon Quality Metrics -- 1.5.2 Performance Indicators -- 1.5.3 Results -- 1.6 Mesh Quality Indicators -- 1.6.1 Definition -- 1.6.2 Results -- 1.7 PEMesh Benchmarking Tool -- References -- 2 On the Implementation of Virtual Element Method for Nonlinear Problems over Polygonal Meshes -- 2.1 Introduction -- 2.1.1 Structure of the Chapter -- 2.1.2 Basic Notation -- 2.2 Governing Equations -- 2.3 Virtual Element Framework -- 2.4 Computation of the Projection Operators and Discrete Bilinear Forms -- 2.5 Fully Discrete Scheme -- 2.6 Implementation -- 2.7 Numerical Examples -- 2.8 Conclusion -- References -- 3 Discrete Hessian Complexes in Three Dimensions -- 3.1 Introduction -- 3.2 Matrix and Vector Operations -- 3.2.1 Matrix-Vector Products -- 3.2.2 Differentiation -- 3.2.3…
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