Spectral and High Order Methods for Partial Differential Equations

Table of Contents

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   Book Overview
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   Chapter 1 hp-FEM for the Contact Problem with Tresca Friction in Linear Elasticity: The Primal Formulation
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   Chapter 2 On Multivariate Chebyshev Polynomials and Spectral Approximations on Triangles
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   Chapter 3 Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
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   Chapter 4 Hybridizable Discontinuous Galerkin Methods
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   Chapter 5 Multivariate Modified Fourier Expansions
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   Chapter 6 Constraint Oriented Spectral Element Method
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   Chapter 7 Convergence Rates of Sparse Tensor GPC FEM for Elliptic sPDEs
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   Chapter 8 A Conservative Spectral Element Method for Curvilinear Domains
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    Chapter 9 An Efficient Control Variate Method for Parametrized Expectations
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    Chapter 10 A Proof, Based on the Euler Sum Acceleration, of the Recovery of an Exponential (Geometric) Rate of Convergence for the Fourier Series of a Function with Gibbs Phenomenon
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    Chapter 11 A Seamless Reduced Basis Element Method for 2D Maxwell’s Problem: An Introduction
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    Chapter 12 An hp-Nitsche’s Method for Interface Problems with Nonconforming Unstructured Finite Element Meshes
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    Chapter 13 Hybrid Explicit–Implicit Time Integration for Grid-Induced Stiffness in a DGTD Method for Time Domain Electromagnetics
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    Chapter 14 High-Order Quasi-Uniform Approximation on the Sphere Using Fourier-Finite-Elements
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    Chapter 15 An hp Certified Reduced Basis Method for Parametrized Parabolic Partial Differential Equations
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    Chapter 16 Highly Accurate Discretization of the Navier–Stokes Equations in Streamfunction Formulation
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    Chapter 17 Edge Functions for Spectral Element Methods
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    Chapter 18 Modeling Effects of Electromagnetic Waves on Thin Wires with a High-Order Discontinuous Galerkin Method
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    Chapter 19 A Hybrid Method for the Resolution of the Gibbs Phenomenon
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    Chapter 20 Numerical Simulation of Fluid–Structure Interaction in Human Phonation: Verification of Structure Part
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    Chapter 21 A New Spectral Method on Triangles
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    Chapter 22 The Reduced Basis Element Method: Offline-Online Decomposition in the Nonconforming, Nonaffine Case
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    Chapter 23 The Challenges of High Order Methods in Numerical Weather Prediction
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    Chapter 24 GMRES for Oscillatory Matrix-Valued Differential Equations
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    Chapter 25 Sensitivity Analysis of Heat Exchangers Using Perturbative Methods
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    Chapter 26 Spectral Element Approximation of the Hodge-⋆ Operator in Curved Elements
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    Chapter 27 Uncertainty Propagation for Systems of Conservation Laws, High Order Stochastic Spectral Methods
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    Chapter 28 Reduced Basis Approximation for Shape Optimization in Thermal Flows with a Parametrized Polynomial Geometric Map
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    Chapter 29 Constrained Approximation in hp-FEM: Unsymmetric Subdivisions and Multi-Level Hanging Nodes
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    Chapter 30 High Order Filter Methods for Wide Range of Compressible Flow Speeds
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    Chapter 31 hp-Adaptive CEM in Practical Applications
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    Chapter 32 Anchor Points Matter in ANOVA Decomposition
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    Chapter 33 An Explicit Discontinuous Galerkin Scheme with Divergence Cleaning for Magnetohydrodynamics
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    Chapter 34 High Order Polynomial Interpolation of Parameterized Curves
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    Chapter 35 A New Discontinuous Galerkin Method for the Navier–Stokes Equations
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    Chapter 36 A $${P}_{n}^{\alpha ,\beta}$$ -Based Method for Linear Nonconstant Coefficients High Order Eigenvalue Problems
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    Chapter 37 Spectral Element Discretization of Optimal Control Problems
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    Chapter 38 Applications of High Order Methods to Vortex Instability Calculations
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    Chapter 39 Entropy Viscosity Method for High-Order Approximations of Conservation Laws
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    Chapter 40 High-Order Accurate Numerical Solution of Incompressible Slip Flow and Heat Transfer in Microchannels
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    Chapter 41 Spectral Methods for Time-Dependent Variable-Coefficient PDE Based on Block Gaussian Quadrature
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    Chapter 42 The Spectral Element Method Used to Assess the Quality of a Global C 1 Map
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    Chapter 43 Stabilization of the Spectral-Element Method in Turbulent Flow Simulations
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    Chapter 44 The Spectral-Element and Pseudo-Spectral Methods: A Comparative Study
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    Chapter 45 Adaptive Spectral Filtering and Digital Total Variation Postprocessing for the DG Method on Triangular Grids: Application to the Euler Equations
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    Chapter 46 BDDC and FETI-DP Preconditioners for Spectral Element Discretizations of Almost Incompressible Elasticity
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    Chapter 47 A Two-Dimensional DG-SEM Approach to Investigate Resonance Frequencies and Sound Radiation of Woodwind Instruments
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    Chapter 48 Spectral Properties of Discontinuous Galerkin Space Operators on Curved Meshes
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    Chapter 49 Post-Processing of Marginally Resolved Spectral Element Data