Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations - Pernet, Sébastien

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Résumé :
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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Biographie:
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Sommaire:
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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