Finite Element Methods for Eigenvalue Problems. (2016)

• Record Type: Book
• Other Names: (Mathematics teacher), Sun, Jiguang
• Contents: Cover; Half Title; Title Page; Copyright Page; Contents; Preface; List of Figures; List of Tables; 1 Functional Analysis; 1.1 Basics; 1.1.1 Metric Spaces, Banach Spaces and Hilbert Spaces; 1.1.2 Linear Operators; 1.1.3 Spectral Theory of Linear Operators; 1.2 Sobolev Spaces; 1.2.1 Basic Concepts; 1.2.2 NegativeNorm; 1.2.3 Trace Spaces; 1.3 Variational Formulation; 1.4 Abstract Spectral Approximation Theories; 1.4.1 Theory of Descloux, Nassif, and Rappaz; 1.4.2 Theory of Babuška and Osborn; 1.4.3 Variationally Formulated Eigenvalue Problems; 2 Finite Elements; 2.1 Introduction; 2.1.1 Meshes. 2.1.2 Lagrange Elements2.2 Quadrature Rules; 2.2.1 Gaussian Quadratures; 2.2.2 Quadratures for a Triangle; 2.2.3 Quadrature Rules for Tetrahedra; 2.3 Abstract Convergence Theory; 2.3.1 Céa's Lemma; 2.3.2 Discrete Mixed Problems; 2.3.3 Inverse Estimates; 2.4 Approximation Properties; 2.5 Appendix: Implementation of Finite Elements in 1D; 3 The Laplace Eigenvalue Problem; 3.1 Introduction; 3.2 Lagrange Elements for the Source Problem; 3.3 Convergence Analysis; 3.4 Numerical Examples; 3.5 Appendix: Implementation of the Linear Lagrange Element; 3.5.1 Triangular Meshes; 3.5.2 Matrices Assembly. 3.5.3 Boundary Conditions3.5.4 Sample Codes; 4 The Biharmonic Eigenvalue Problem; 4.1 Introduction; 4.2 The Argyris Element; 4.2.1 The Discrete Problem; 4.2.2 Numerical Examples; 4.3 A Mixed Finit Element Method; 4.3.1 Abstract Framework; 4.3.2 The Ciarlet-Raviart Method; 4.3.3 Numerical Examples; 4.4 The Morley Element; 4.4.1 Abstract Theory; 4.4.2 The Morley Element; 4.4.3 Numerical Examples; 4.5 A Discontinuous Galerkin Method; 4.5.1 Biharmonic Eigenvalue Problems; 4.5.2 C[sup(0)] Interior Penalty Galerkin Method; 4.5.3 Numerical Examples; 4.5.4 Comparisons of Different Methods. 4.6 C[sup(0)] IPG for a Fourth Order Problem4.6.1 The Source Problem; 4.6.2 The Eigenvalue Problem; 4.6.3 Numerical Examples; 4.7 Appendix: MATLAB Code for the Mixed Method; 5 The Maxwell's Eigenvalue Problem; 5.1 Introduction; 5.2 The Maxwell's Eigenvalue Problem; 5.2.1 Preliminaries; 5.2.2 The Curl-curl Problem; 5.2.3 Divergence-conforming Elements; 5.2.4 Curl-conforming Edge Elements; 5.2.5 Convergence Analysis; 5.2.6 The Eigenvalue Problem; 5.2.7 An Equivalent Eigenvalue Problem; 5.2.8 Numerical Examples; 5.3 The Quad-curl Eigenvalue Problem; 5.3.1 The Quad-curl Problem. 5.3.2 The Quad-curl Eigenvalue Problem5.3.3 Numerical Examples; 6 The Transmission Eigenvalue Problem; 6.1 Introduction; 6.2 Existence of Transmission Eigenvalues; 6.2.1 Spherically Stratified Media; 6.2.2 General Media; 6.2.3 Non-existence of Imaginary Transmission Eigenvalues; 6.2.4 Complex Transmission Eigenvalues; 6.3 Argyris Element for Real Transmission Eigenvalues; 6.3.1 A Fourth Order Reformulation; 6.3.2 Bisection Method; 6.3.3 Secant Method; 6.3.4 Some Discussions; 6.4 A Mixed Method Using The Argyris Element; 6.4.1 The Mixed Formulation; 6.4.2 Convergence Analysis.
• Publisher Details: Place of publication not identified : Taylor and Francis
• Publication Date: 2016
• Extent: 1 online resource, illustrations
• Subjects: 518.3; MATHEMATICS / Number Systems; Eigenvalues; Eigenvalues; SCIENCE / Mechanics / General; Electronic books
• Languages: English
• ISBNs: 1482254654; 9781482254655
• Related ISBNs: 1482254646
• Notes: Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.