This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

Proceedings of leading conference in high-order methods Wide coverage of high-order numerical techniques and their applications Contributions from internationally leading experts in the field Presentation of the state-of-the-art and extensive bibliography

Inhalt

Stability of wall boundary condition procedures for discontinuous Galerkin spectral element approximations of the compressible Euler equations.- On the order reduction of entropy stable DGSEMfor the compressible Euler equations.- A review of regular decompositions of vector fields continuous, discrete, and structure-preserving.- Model reduction by separation of variables: a comparison between hierarchical model reduction and proper generalized decomposition.- Recurrence relations for a family of orthogonal polynomials on a triangle.- Greedy kernel methods for center manifold approximation.- An improved error inhibiting block one-step method with radial basis function approximation for ODEs.- Hermite methods in time.- HPS accelerated spectral solvers for time dependent problems: algorithms.- On the use of hermite functions for the Vlasov-Poisson system.- HPS accelerated spectral solvers for time dependent problems: numerical experiments.- High-order finite element methods for interface problems: theory and implementations.- Stabilised hybrid discontinuous galerkin methods for the Stokes problem with non-standard boundary conditions.- RBF based CWENO method.- discrete equivalence of adjoint Neumann-Dirichlet div-grad and grad-div equations in curvilinear 3D domains.- A conservative hybrid method for Darcy flow.- High-order mesh generation based on optimal affine combinations of nodal positions.- Sparse spectral-element methods for the helically reduced Einstein equations.- Spectral analysis of isogeometric discretizations of 2D curl-div Problems with general geometry.- Performance of preconditioners for large-scale simulations using Nek5000.- Two decades old entropy stable method for the Euler equations revisited.- A mimetic spectral element method for free surface flows.- Spectral/hp methodology study for iLES-SVV on an Ahmed body.- A highorder discontinuous Galerkin solver for multiphase flows.- High-Order propagation of jet noise on a tetrahedral mesh using large eddy simulation sources.- Dynamical degree adaptivity for DG-LES models.- A novel eight-order diffusive scheme for unstructured polyhedral grids using the weighted least-squares method.- An explicit mapped tent pitching scheme for Maxwell equations.- Viscous diffusion effects in the eigenanalysis of (hybridisable) DG methods.- Spectral Galerkin method for solving Helmholtz and Laplace Dirichlet problems on multiple open arcs.- Explicit polynomial Trefftz-DG method for space-time elasto-acoustics.- An hp-adaptive iterative linearization discontinuous-Galerkin FEM for quasilinear elliptic boundary value problems.- Erosion Wear evaluation using Nektar++.- An inexact Petrov-Galerkin approximation for gas transport in pipeline networks.- New preconditioners for semi-linear PDE-constrained optimal control in annular geometries.- DIRK schemes with high weak stage order.- Scheme for evolutionary Navier-Stokes-Fourier system with temperature dependent material properties based on spectral/hp elements.- Implicit large eddy simulations for NACA0012 airfoils using compressible and incompressible discontinuous Galerkin solvers.- SAV method applied to fractional Allen-Cahn equation.- A first meshless approach to simulation of the elastic behaviour of the diaphragm.- An explicit hybridizable discontinuous Galerkin method for the 3D timedomain Maxwell equations.- Entropy conserving and kinetic energy preserving numerical methods for the Euler equations using summation-by-parts operators.- Multiwavelet troubled-cell indication: a comparison of utilizing theory versus outlier detection.- An anisotropic p-adaptation multigrid scheme for discontinuous Galerkin methods.- A spectral element reduced basis method for Navier-Stokes equations with geometric variations.- Iterative spectral mollification and conjugation for successive edge detection.- Small trees for high order Whitney elements.- Non-conforming elements inNek5000: pressure preconditioning and parallel performance.- Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit.- On the convergence rate of Hermite-Fejer interpolation.