Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods | Paper Citation Record

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This paper cites A new front tracking sche me for the ultra-relativistic Euler equations.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A new front tracking sche me for the ultra-relativistic Euler equations

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This paper cites Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems

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This paper cites Relativistic ﬂuid dynamic s: physics for many diﬀerent scales.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Relativistic ﬂuid dynamic s: physics for many diﬀerent scales

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators

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This paper cites Julia: A Fresh Approach to Numerical Computing.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Julia: A Fresh Approach to Numerical Computing

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This paper cites p4est: Scala ble algorithms for parallel adaptive mesh reﬁnement on forests of octrees.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods p4est: Scala ble algorithms for parallel adaptive mesh reﬁnement on forests of octrees

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This paper cites Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Disc ontinuous Interfaces.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Disc ontinuous Interfaces

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This paper cites On discretely entropy conservative and entrop y stable discontinuous Galerkin methods.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods On discretely entropy conservative and entrop y stable discontinuous Galerkin methods

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This paper cites Kinetic Energy Preserving and Entrop y Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Kinetic Energy Preserving and Entrop y Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Conservation laws for relativistic ﬂuid dyna mics

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This paper cites Entropy stable high order discon tinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation law s.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Entropy stable high order discon tinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation law s

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This paper cites Embedded pairs fo r optimal explicit strong stability preserving Runge-Kutta methods.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Embedded pairs fo r optimal explicit strong stability preserving Runge-Kutta methods

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Recent developments in mathematical aspe cts of relativistic ﬂuids

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This paper cites A wel l-balanced discontinuous Galerkin method for the ﬁrst–order Z4 formulation of the Einstein–Euler system.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A wel l-balanced discontinuous Galerkin method for the ﬁrst–order Z4 formulation of the Einstein–Euler system

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This paper cites Revi ew of summation-by-parts opera- tors with simultaneous approximation terms for the numerical solution of partial diﬀerential equations.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Revi ew of summation-by-parts opera- tors with simultaneous approximation terms for the numerical solution of partial diﬀerential equations

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This paper cites High-order entropy sta ble ﬁnite diﬀerence schemes for nonlinear conservation laws: Finite domains.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods High-order entropy sta ble ﬁnite diﬀerence schemes for nonlinear conservation laws: Finite domains

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This paper cites Relativistic barotropic ﬂuids: a God unov-Boillat formulation for their dy- namics and a discussion of two special classes.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Relativistic barotropic ﬂuids: a God unov-Boillat formulation for their dy- namics and a discussion of two special classes

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This paper cites On shock proﬁles in four-ﬁe ld formulations of dissipative relativistic ﬂuid dynamics.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods On shock proﬁles in four-ﬁe ld formulations of dissipative relativistic ﬂuid dynamics

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This paper cites A well balanced ﬁn ite volume scheme for general relativity.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A well balanced ﬁn ite volume scheme for general relativity

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This paper cites A Skew-Symmetric Discontinuous Galerk in Spectral Element Discretization and Its Relation to SBP-SAT Finite Diﬀerence Methods.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A Skew-Symmetric Discontinuous Galerk in Spectral Element Discretization and Its Relation to SBP-SAT Finite Diﬀerence Methods

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This paper cites Split Fo rm Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compress ible Euler Equations.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Split Fo rm Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compress ible Euler Equations

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This paper cites Groah, J.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Groah, J

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This paper cites A provably entropy stable subcell shock capturing approach for high or der split form DG for the com- pressible Euler equations.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A provably entropy stable subcell shock capturing approach for high or der split form DG for the com- pressible Euler equations

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This paper cites Constructing stable, high-order finite-difference operators on point clouds over complex geometries.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Constructing stable, high-order finite-difference operators on point clouds over complex geometries

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Entropy-stable, high-order summation- by-parts discretizations without inter- face penalties

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Multi dimensional Summation-By- Parts Operators: General Theory and Application to Simplex Elements

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This paper cites A Flux Reconstruction Approach to High-Or der Schemes Including Discontin- uous Galerkin Methods.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A Flux Reconstruction Approach to High-Or der Schemes Including Discontin- uous Galerkin Methods

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Aﬀordable, entropy-consisten t Euler ﬂux functions II: Entropy production at shocks

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This paper cites Assessing st andard and kinetic energy conserv- ing volume ﬂuxes in discontinuous Galerkin formulations fo r marginally resolved Navier- Stokes ﬂows.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Assessing st andard and kinetic energy conserv- ing volume ﬂuxes in discontinuous Galerkin formulations fo r marginally resolved Navier- Stokes ﬂows

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Contractivity of Runge-Kutta me thods

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Finite Element and Finite D iﬀerence Methods for Hyperbolic Partial Diﬀerential Equations

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This paper cites Radially symme tric solutions of the ultra- relativistic Euler equations in several space dimensions.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Radially symme tric solutions of the ultra- relativistic Euler equations in several space dimensions

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Radially symmetric so lutions of the ultra-relativistic Euler equations

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A BGK-type ﬂux-vecto r splitting scheme for the ultrarelativistic Euler equations

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Kinetic schemes for t he ultra-relativistic Euler equa- tions

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Second-order accur ate kinetic schemes for the ultra- relativistic Euler equations

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Self-similar solutions of the radially symmet ric relativistic Euler equations

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Fully Discret e, Entropy Conservative Schemes of Arbitrary Order

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods An adaptive ﬁnite element scheme for transie nt problems in CFD

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Finite volume approximatio ns and strict stability for hyperbolic problems

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Finite volume methods, unstruc- tured meshes and strict stability for hyperbolic problems

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Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Ultra-relativistic limit o f extended thermodynamics of rareﬁed polyatomic gas

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This paper cites DiﬀerentialEquations.jl – A Performant and Feature-Rich Ecosys- tem for Solving Diﬀerential Equations in Julia.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods DiﬀerentialEquations.jl – A Performant and Feature-Rich Ecosys- tem for Solving Diﬀerential Equations in Julia

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This paper cites A Note on Numerical Fluxes Conserving a Memb er of Harten’s One-Parameter Family of Entropies for the Compressible Euler Equations.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A Note on Numerical Fluxes Conserving a Memb er of Harten’s One-Parameter Family of Entropies for the Compressible Euler Equations

Reference 48

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Observation 1095f35b-9a92-425b-8521-7a4cefaa0db9 · outbound

This paper cites Comparison of some Entropy Conservative Numerical Fluxes for the Euler Equations.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Comparison of some Entropy Conservative Numerical Fluxes for the Euler Equations

Reference 49

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Observation bde2505a-f2c2-4e61-be0b-356e55edff54 · outbound

This paper cites Entropy Conserving and Kinetic Energy Pres erving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Entropy Conserving and Kinetic Energy Pres erving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators

Reference 50

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Observation a6bec274-f768-4cb5-804c-ef566791c987 · outbound

This paper cites Generalised Summation-by-Parts Operato rs and Entropy Stability of Numeri- cal Methods for Hyperbolic Balance Laws.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Generalised Summation-by-Parts Operato rs and Entropy Stability of Numeri- cal Methods for Hyperbolic Balance Laws

Reference 51

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Observation af0bdb59-08c8-466c-9de2-f1b68e15f48f · outbound

This paper cites Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

Reference 52

Resolution: verified exact; local_arxiv, observed 2026-08-05T14:28:10.235694Z

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Observation b36adce4-b241-4603-a676-d0ab0ec7aae3 · outbound

This paper cites Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes

Reference 53

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Observation 153ad636-577a-44de-8483-4671c3b21718 · outbound

This paper cites Summation-by-parts operators for correction procedure via reconstruction.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Summation-by-parts operators for correction procedure via reconstruction

Reference 54

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Observation 73983580-3e26-4b6c-838c-3627092aea72 · outbound

This paper cites Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing

Reference 55

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Observation 199a13e1-0ba7-4b03-ada1-2e9f0a3bbc47 · outbound

This paper cites Ruggeri and M.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Ruggeri and M

Reference 56

Resolution: verified exact; doi, observed 2026-08-05T14:28:07.407243Z

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Observation 1219c827-89d0-4a78-9ded-42e95d43d186 · outbound

This paper cites Classical and ultrarelativist ic limits of the Riemann problem for the relativistic Euler ﬂuid with Synge energy.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Classical and ultrarelativist ic limits of the Riemann problem for the relativistic Euler ﬂuid with Synge energy

Reference 57

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Observation 97c8c5f3-c8c8-4bf7-9f2e-5bf8a16ebeb7 · outbound

This paper cites Nonlinear hyperbolic waves in relativistic gases of massive particles with Synge energy.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Nonlinear hyperbolic waves in relativistic gases of massive particles with Synge energy

Reference 58

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Observation e1f9cf07-451b-451f-bb8b-00ac57dd21e7 · outbound

This paper cites A purely hyper- bolic discontinuous Galerkin approach for self-gravitati ng gas dynamics.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A purely hyper- bolic discontinuous Galerkin approach for self-gravitati ng gas dynamics

Reference 59

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This paper cites Skew-symmetric sp litting and stability of high order central schemes.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Skew-symmetric sp litting and stability of high order central schemes

Reference 60

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Observation c730f96b-87eb-4d4f-8891-2a531307c239 · outbound

This paper cites an unresolved cited work.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Unresolved cited work

Reference 61

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Observation 09590ac8-9c52-4786-83b4-2601a9d6a7b5 · outbound

This paper cites General relativistic self-s imilar waves that induce an anomalous acceleration into the standard model of cosmology.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods General relativistic self-s imilar waves that induce an anomalous acceleration into the standard model of cosmology

Reference 62

Resolution: verified exact; doi, observed 2026-08-05T14:28:06.714882Z

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This paper cites Global solutions of the relat ivistic Euler equations.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Global solutions of the relat ivistic Euler equations

Reference 63

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Observation f7625f0c-0b89-4277-a51e-4c84c09a7b9b · outbound

This paper cites Relativistic detonation waves and b ubble growth in false vacuum decay.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Relativistic detonation waves and b ubble growth in false vacuum decay

Reference 64

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Observation 4b601789-0c10-4df7-bdb8-d73b631940fc · outbound

This paper cites Summation by Parts for Finite Diﬀerence App roximations for /u1D451//u1D451/u1D465.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Summation by Parts for Finite Diﬀerence App roximations for /u1D451//u1D451/u1D465

Reference 65

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Observation 44a1e6cd-e945-4444-9e55-7c9666ba2450 · outbound

This paper cites Review of summation-by-part s schemes for initial-boundary- value problems.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Review of summation-by-part s schemes for initial-boundary- value problems

Reference 66

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Observation b85df4e7-7d82-4d78-8541-b5fadbf927ed · outbound

This paper cites Entropy stability theory for diﬀerence app roximations of nonlinear conservation laws and related time-dependent problems.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Entropy stability theory for diﬀerence app roximations of nonlinear conservation laws and related time-dependent problems

Reference 67

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This paper cites The numerical viscosity of entropy stable s chemes for systems of conservation laws. I.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods The numerical viscosity of entropy stable s chemes for systems of conservation laws. I

Reference 68

Resolution: malformed identifier; doi_truncated, observed 2026-08-05T14:28:06.527596Z

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Observation 2a69b354-5727-42dd-9844-274f736ea2fa · outbound

This paper cites Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-St able Discontinuous Galerkin Methods.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-St able Discontinuous Galerkin Methods

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:28:10.865895Z

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Observation 1f3d944f-f72b-4516-9eb2-e7f85058ced8 · outbound

This paper cites A New Clas s of High-Order Energy Stable Flux Reconstruction Schemes.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A New Clas s of High-Order Energy Stable Flux Reconstruction Schemes

Reference 70

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Observation cc1b59a0-9ed1-4088-8019-b2b920efd25d · outbound

This paper cites On Godunov’s interesting class of system s - The symmetric hyperbolic Eu- ler equations of gas dynamics.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods On Godunov’s interesting class of system s - The symmetric hyperbolic Eu- ler equations of gas dynamics

Reference 71

Resolution: metadata mismatch; raw_fallback, observed 2026-08-05T14:28:10.054383Z

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Observation ff8b808c-925a-495d-93f0-8624459075b5 · outbound

This paper cites Weinberg.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Weinberg

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:28:10.855029Z

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Observation 26075314-4c98-462c-8b5d-f022eb5808a6 · outbound

This paper cites A high order special relativi stic hydrodynamic and magneto- hydrodynamic code with space-time adaptive mesh reﬁnement.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods A high order special relativi stic hydrodynamic and magneto- hydrodynamic code with space-time adaptive mesh reﬁnement

Reference 73

Resolution: verified exact; doi, observed 2026-08-05T14:28:06.301014Z

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Observation c578f43e-be08-4ddf-b4b1-62081efdd559 · outbound

This paper cites Maximum-principle-satisfying and positivity-preserving high- order schemes for conservation laws: survey and new develop ments.

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods Maximum-principle-satisfying and positivity-preserving high- order schemes for conservation laws: survey and new develop ments

Reference 74

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