Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations

Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations by Gary Cohen, Sébastien Pernet.

This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D...

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Bibliographic Details
Main Authors: Cohen, Gary (Author), Pernet, Sébastien (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2017.
Edition:1st ed. 2017.
Series:Scientific Computation,
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
Physics.
Mathematical physics.
Continuum physics.
Mechanics.
Mechanics, Applied.
Computer mathematics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of 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.

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