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.
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.- Hlӝ
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