Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions
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Publication:2673966
DOI10.1016/j.amc.2022.127508OpenAlexW4294591104MaRDI QIDQ2673966
Philipp Öffner, Mária Lukáčová-Medvid'ová
Publication date: 21 September 2022
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2202.10043
convergence analysisEuler equationsdiscontinuous Galerkinstructure preservingdissipative weak solutions
Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) Hyperbolic equations and hyperbolic systems (35Lxx)
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Cites Work
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- High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
- A minimum entropy principle of high order schemes for gas dynamics equations
- Weak-strong uniqueness for measure-valued solutions
- On admissibility criteria for weak solutions of the Euler equations
- A direct Eulerian GRP scheme for compressible fluid flows
- On the symmetric form of systems of conservation laws with entropy
- Extended skew-symmetric form for summation-by-parts operators and varying Jacobians
- Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
- Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements
- Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws
- On the order reduction of entropy stable DGSEM for the compressible Euler equations
- Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems
- A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations
- A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
- Entropy stable, robust and high-order DGSEM for the compressible multicomponent Euler equations
- Reinterpretation and extension of entropy correction terms for residual distribution and discontinuous Galerkin schemes: application to structure preserving discretization
- Convergence of finite volume schemes for the Euler equations via dissipative measure-valued solutions
- Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows
- Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting
- A finite volume scheme for the Euler system inspired by the two velocities approach
- Skew-symmetric entropy stable modal discontinuous Galerkin formulations
- Summation-by-parts operators for correction procedure via reconstruction
- Discontinuous Galerkin method for hyperbolic equations involving \(\delta \)-singularities: negative-order norm error estimates and applications
- 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
- Uniqueness of dissipative solutions to the complete Euler system
- A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods
- Error estimates to smooth solutions of semi‐discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws
- Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
- Weak-strong uniqueness for measure-valued solutions of some compressible fluid models
- Correction to: “Uniqueness failure for entropy solutions of hyperbolic systems of conservation laws”
- Compensated Compactness and General Systems of Conservation Laws
- Uniqueness failure for entropy solutions of hyperbolic systems of conservation laws
- Convex Entropies and Hyperbolicity for General Euler Equations
- A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art
- Second-Order Invariant Domain Preserving Approximation of the Euler Equations Using Convex Limiting
- Numerical Analysis of Compressible Fluid Flows
- On Convergence of Numerical Solutions for the Compressible MHD System with Exactly Divergence-Free Magnetic Field
- Computing oscillatory solutions of the Euler system via 𝒦-convergence
- Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations
- Efficient Entropy Stable Gauss Collocation Methods
- On uniqueness of dissipative solutions to the isentropic Euler system
- Weak solutions for Euler systems with non-local interactions
- Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations
- Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements
- Error Estimates to Smooth Solutions of Runge–Kutta Discontinuous Galerkin Method for Symmetrizable Systems of Conservation Laws