Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations. (2017)

• Record Type: Book
• Further Information: Note: By Gary Cohen, Sébastien Pernet.
• Authors: Cohen, Gary; Pernet, Sébastien
• Other Names: École nationale supérieure des beaux-arts (France)
• Contents: Classical Continuous Models and their Analysis -- The Basic Equations -- Functional Issues -- Plane Wave Solutions -- Definition of Different Types of Finite Elements -- 1D Mass-Lumping and Spectral Elements -- Quadrilaterals and Hexahedra -- Triangles and Tetrahedra -- Purely 3D Elements -- Tetrahedral and Triangular Edge Elements -- Hexahedral and Quadrilateral Edge Elements -- H(div) Finite Elements -- Other Mixed Elements -- Hexahedral and Quadrilateral Spectral Elements for Acoustic Waves -- Second Order Formulation of the Acoustics Equation -- First Order Formulation of the Acoustics Equation -- Comparison of the Methods -- Dispersion Relation -- Reflection-Transmission by a Discontinuous Interface -- hp-a priori Error Estimates -- The Linear Elastodynamics System -- Discontinuous Galerkin Methods -- General Formulation for Linear Hyperbolic Problems -- Approximation by Triangles and Tetrahedra -- Approximation by Quadrilaterals and Hexahedra -- Comparison of the DG Methods for Maxwell's Equations -- Plane Wave Analysis -- Interior Penalty Discontinuous Galerkin Methods -- The Maxwell's System and Spurious Modes.-A First Model and its Approximation -- A Second Model and its Approximations -- Suppressing Spurious Modes -- Error Estimates for DGM -- Approximating Unbounded Domains -- Absorbing Boundary Conditions (ABC) -- Perfectly Matched Layers (PML) -- Time Approximation -- Schemes with a Constant Time-Step -- Local Time Stepping -- Some Complex Models -- The Linearized Euler Equations -- The Linear Cauchy-Poisson Problem -- Vibrating Thin Plates -- References -- Bibliography.
• Publisher Details: Dordrecht : Springer Netherlands Imprint Springer
• Publication Date: 2017
• Extent: 1 online resource (XVII, 381 pages 79 illustrations, 39 illustrations in color.)
• Subjects: 519; Engineering; Mathematical physics; Computer science -- Mathematics; Physics; Field theory (Physics); Applied mathematics; Engineering mathematics; Continuum mechanics; Finite element method; Galerkin methods; Galerkin methods; Finite element method; Computer science -- Mathematics; Continuum mechanics; Engineering; Engineering mathematics; Field theory (Physics); Mathematical physics; Physics; Engineering; Appl.Mathematics/Computational Methods of Engineering; Numerical and Computational Physics; Mathematical Applications in the Physical Sciences; Classical Continuum Physics; Continuum Mechanics and Mechanics of Materials; Computational Science and Engineering; Electronic book; Electronic books
• Languages: English
• ISBNs: 9401777616; 9789401777612; 9789401777599; 9401777594
• Notes: Note: Includes bibliographical references at the end of each chapters.; 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.