Hesthaven J.S., Rønquist E.M. (eds.) Spectral and High Order Methods for Partial Differential Equations

Berlin: Springer, 2011. - 530p.The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.hp -FEM for the Contact Problem with Tresca Friction in Linear Elasticity: The Primal Formulation
On Multivariate Chebyshev Polynomials and Spectral Approximations on Triangles
Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
Hybridizable Discontinuous Galerkin Methods
Multivariate Modified Fourier Expansions
Constraint Oriented Spectral Element Method
Convergence Rates of Sparse Tensor GPC FEM for Elliptic sPDEs
A Conservative Spectral Element Method for Curvilinear Domains
An Efficient Control Variate Method for Parametrized Expectations
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
A Seamless Reduced Basis Element Method for 2D Maxwell’s Problem: An Introduction
An hp -Nitsche’s Method for Interface Problems with Nonconforming Unstructured Finite Element Meshes
Hybrid Explicit–Implicit Time Integration for Grid-Induced Stiffness in a DGTD Method for Time Domain Electromagnetics
High-Order Quasi-Uniform Approximation on the Sphere Using Fourier-Finite-Elements
An hp Certified Reduced Basis Method for Parametrized Parabolic Partial Differential Equations
Highly Accurate Discretization of the Navier–Stokes Equations in Streamfunction Formulation
Edge Functions for Spectral Element Methods
Modeling Effects of Electromagnetic Waves on Thin Wires with a High-Order Discontinuous Galerkin Method
A Hybrid Method for the Resolution of the Gibbs Phenomenon
Numerical Simulation of Fluid–Structure Interaction in Human Phonation: Verification of Structure Part
A New Spectral Method on Triangles
The Reduced Basis Element Method: Offline-Online Decomposition in the Nonconforming, Nonaffine Case
The Challenges of High Order Methods in Numerical Weather Prediction
GMRES for Oscillatory Matrix-Valued Differential Equations
Sensitivity Analysis of Heat Exchangers Using Perturbative Methods
Spectral Element Approximation of the Hodge-⋆ Operator in Curved Elements
Uncertainty Propagation for Systems of Conservation Laws, High Order Stochastic Spectral Methods
Reduced Basis Approximation for Shape Optimization in Thermal Flows with a Parametrized Polynomial Geometric Map
Constrained Approximation in hp -FEM: Unsymmetric Subdivisions and Multi-Level Hanging Nodes
High Order Filter Methods for Wide Range of Compressible Flow Speeds
hp -Adaptive CEM in Practical Applications
Anchor Points Matter in ANOVA Decomposition
An Explicit Discontinuous Galerkin Scheme with Divergence Cleaning for Magnetohydrodynamics
High Order Polynomial Interpolation of Parameterized Curves
A New Discontinuous Galerkin Method for the Navier–Stokes Equations
A $${P}_{n}^{\alpha ,\beta}$$ -Based Method for Linear Nonconstant Coefficients High Order Eigenvalue Problems
Spectral Element Discretization of Optimal Control Problems
Applications of High Order Methods to Vortex Instability Calculations
Entropy Viscosity Method for High-Order Approximations of Conservation Laws
High-Order Accurate Numerical Solution of Incompressible Slip Flow and Heat Transfer in Microchannels
Spectral Methods for Time-Dependent Variable-Coefficient PDE Based on Block Gaussian Quadrature
The Spectral Element Method Used to Assess the Quality of a Global C 1 Map
Stabilization of the Spectral-Element Method in Turbulent Flow Simulations
The Spectral-Element and Pseudo-Spectral Methods: A Comparative Study
Adaptive Spectral Filtering and Digital Total Variation Postprocessing for the DG Method on Triangular Grids: Application to the Euler Equations
BDDC and FETI-DP Preconditioners for Spectral Element Discretizations of Almost Incompressible Elasticity
A Two-Dimensional DG-SEM Approach to Investigate Resonance Frequencies and Sound Radiation of Woodwind Instruments
Spectral Properties of Discontinuous Galerkin Space Operators on Curved Meshes
Post-Processing of Marginally Resolved Spectral Element Data