Generalised summation-by-parts operators and variable coefficients
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Publication:1640859
DOI10.1016/j.jcp.2018.02.021zbMath1395.65054arXiv1705.10541OpenAlexW2618630098MaRDI QIDQ1640859
Publication date: 14 June 2018
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1705.10541
First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)
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Cites Work
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- PyFR: an open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach
- High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
- Review of summation-by-parts schemes for initial-boundary-value problems
- \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
- Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations
- A generalized framework for nodal first derivative summation-by-parts operators
- Summation-by-parts operators and high-order quadrature
- Entropy viscosity method for nonlinear conservation laws
- On the quadrature and weak form choices in collocation type discontinuous Galerkin spectral element methods
- A new class of high-order energy stable flux reconstruction schemes
- 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
- A family of fourth-order entropy stable nonoscillatory spectral collocation schemes for the 1-D Navier-Stokes equations
- A comparison of the discontinuous-Galerkin- and spectral-difference-method on triangulations using PKD polynomials
- Stable and accurate artificial dissipation
- A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids
- Shock capturing with PDE-based artificial viscosity for DGFEM. I: Formulation
- Conservative finite difference formulations, variable coefficients, energy estimates and artificial dissipation
- Summation by parts for finite difference approximations for \(d/dx\)
- The stability of numerical boundary treatments for compact high-order finite-difference schemes
- Boundary procedures for summation-by-parts operators
- On coordinate transformations for summation-by-parts operators
- Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
- From continuous recovery to discrete filtering in numerical approximations of conservation laws
- Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
- High-order methods for computational fluid dynamics: a brief review of compact differential formulations on unstructured grids
- An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
- Extended skew-symmetric form for summation-by-parts operators and varying Jacobians
- On conservation and stability properties for summation-by-parts schemes
- Shallow water equations: split-form, entropy stable, well-balanced, and positivity preserving numerical methods
- On the stability definition of difference approximations for the initial boundary value problem
- Finite volume methods, unstructured meshes and strict stability for hyperbolic problems
- Summation-by-parts operators for correction procedure via reconstruction
- Vanishing viscosity solutions of nonlinear hyperbolic systems
- 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
- Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: theory and boundary conditions
- Numerical aspects of TV flow
- Metric identities and the discontinuous spectral element method on curvilinear meshes
- An extended range of stable-symmetric-conservative flux reconstruction correction functions
- Image Processing for Numerical Approximations of Conservation Laws: Nonlinear Anisotropic Artificial Dissipation
- A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
- Time-Dependent Problems and Difference Methods
- An extended Discontinuous Galerkin and Spectral Difference Method with modal filtering
- Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws
- An Energy Stable Discontinuous Galerkin Spectral Element Discretization for Variable Coefficient Advection Problems
- Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
- Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Subcells
- A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss–Lobatto Discontinuous Galerkin Spectral Element Methods
- Application of spectral filtering to discontinuous Galerkin methods on triangulations
- Filtering in Legendre spectral methods
- Implementing Spectral Methods for Partial Differential Equations
- Error Bounded Schemes for Time-dependent Hyperbolic Problems
- Taming the CFL Number for Discontinuous Galerkin Methods on Structured Meshes
- Riemann Solvers, the Entropy Condition, and Difference
- The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
- Convergence of Spectral Methods for Nonlinear Conservation Laws
- Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
- Finite Volume Methods for Hyperbolic Problems
- Fully Discrete, Entropy Conservative Schemes of ArbitraryOrder
- Data analysis and entropy steered discrete filtering for the numerical treatment of conservation laws
- 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
- A kinetic energy preserving nodal discontinuous Galerkin spectral element method
- Highly Efficient Strong Stability-Preserving Runge–Kutta Methods with Low-Storage Implementations
- Spectral Methods
- Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements
- A Method for the Numerical Calculation of Hydrodynamic Shocks
- From suitable weak solutions to entropy viscosity
- Finite volume approximations and strict stability for hyperbolic problems
