“In this book finite elements and discontinuous Galerkin (DG) methods are employed for the solution of wave equations. The book consists of a preface and eight chapters. Each chapter concludes with a list of references. It is an excellent reference for researchers working on numerical solutions of transient wave equations. It can also be used as a textbook for a graduate course … .” (Beny Neta, Mathematical Reviews, April, 2017)“This monograph presents much of the progress made during the last two decades in the numerical solution of hyperbolic equations like the acoustics and Maxwell's equation as well as in linear elastodynamic systems. … the book is full of mathematical analysis, but also manypractical aspects and a lot of numerical results are given. … the book may be also quite useful for practitioners.” (Rolf Dieter Grigorieff, zbMATH 1360.65233, 2017)

• 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.

“In this book finite elements and discontinuous Galerkin (DG) methods are employed for the solution of wave equations. The book consists of a preface and eight chapters. Each chapter concludes with a list of references. It is an excellent reference for researchers working on numerical solutions of transient wave equations. It can also be used as a textbook for a graduate course … .” (Beny Neta, Mathematical Reviews, April, 2017)“This monograph presents much of the progress made during the last two decades in the numerical solution of hyperbolic equations like the acoustics and Maxwell's equation as well as in linear elastodynamic systems. … the book is full of mathematical analysis, but also manypractical aspects and a lot of numerical results are given. … the book may be also quite useful for practitioners.” (Rolf Dieter Grigorieff, zbMATH 1360.65233, 2017)

• 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.