Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points
DOI10.1016/j.apnum.2019.12.020zbMath1434.65180arXiv2001.00507OpenAlexW2997883207WikidataQ126418942 ScholiaQ126418942MaRDI QIDQ2301387
Publication date: 24 February 2020
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2001.00507
numerical integrationhyperbolic conservation lawshigh-order methodsdiscontinuous Galerkin methodsdiscrete orthogonal polynomialsdiscrete least squaresscattered nodes
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical quadrature and cubature formulas (65D32)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
- A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions
- A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- Family of spectral filters for discontinuous problems
- Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations
- The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
- Summation by parts for finite difference approximations for \(d/dx\)
- De-aliasing on non-uniform grids: algorithms and applications.
- High order schemes for hyperbolic problems using globally continuous approximation and avoiding mass matrices
- Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators
- Smooth and compactly supported viscous sub-cell shock capturing for discontinuous Galerkin methods
- A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes
- Stable high-order quadrature rules with equidistant points
- Error boundedness of discontinuous Galerkin methods with variable coefficients
- Summation-by-parts operators for correction procedure via reconstruction
- Error boundedness of discontinuous Galerkin spectral element approximations of hyperbolic problems
- Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
- Strong Stability-Preserving High-Order Time Discretization Methods
- A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
- An extended Discontinuous Galerkin and Spectral Difference Method with modal filtering
- An Energy Stable Discontinuous Galerkin Spectral Element Discretization for Variable Coefficient Advection Problems
- Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Subcells
- Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
- Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples
- How to Avoid Mass Matrix for Linear Hyperbolic Problems
- The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
- The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
- Filtering in Legendre spectral methods
- Implementing Spectral Methods for Partial Differential Equations
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- On a Cell Entropy Inequality for Discontinuous Galerkin Methods
- Total variation diminishing Runge-Kutta schemes
- From Semidiscrete to Fully Discrete: Stability of Runge--Kutta Schemes by The Energy Method
- Finite Volume Methods for Hyperbolic Problems
- Application of modal filtering to a spectral difference method
- Summation by Parts, Projections, and Stability. I
- Summation by Parts, Projections, and Stability. II
- A simple shock‐capturing technique for high‐order discontinuous Galerkin methods
- Highly Efficient Strong Stability-Preserving Runge–Kutta Methods with Low-Storage Implementations
- High Order Edge Sensors with $\ell^1$ Regularization for Enhanced Discontinuous Galerkin Methods
- Necessary and Sufficient Conditions for Equidistant Quadrature Formula
- Discrete Least Squares and Quadrature Formulas