Convergence of the finite volume method on a Schwarzschild background

DOI10.1051/m2an/2019037zbMath1435.35381arXiv1901.10973OpenAlexW2962882239MaRDI QIDQ4972100

Philippe G. LeFloch, Shijie Dong

Publication date: 22 November 2019

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.10973

zbMATH Keywords

convergence analysisweak solutionfinite volume schemeSchwarzschild black holehyperbolic conservation law

Mathematics Subject Classification ID

Black holes (83C57) Shock waves and blast waves in fluid mechanics (76L05) First-order nonlinear hyperbolic equations (35L60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with relativity and gravitational theory (35Q75) Weak solutions to PDEs (35D30) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (1)

A class of well-balanced algorithms for relativistic fluids on a Schwarzschild background

Cites Work

• Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime
• Finite volume schemes on Lorentzian manifolds
• Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime. II
• Measure-valued solutions to conservation laws
• Ergodicity and Hopf-Lax-Oleinik formula for fluid flows evolving around a black hole under a random forcing
• Relativistic Burgers Equations on Curved Spacetimes. Derivation and Finite Volume Approximation
• Traces for Functions of Bounded Variation on Manifolds with Applications to Conservation Laws on Manifolds with Boundary
• Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms
• Convergence of the Finite Volume Method for Multidimensional Conservation Laws
• A simple family of analytical trumpet slices of the Schwarzschild spacetime
• A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime
• A Geometry-Preserving Finite Volume Method for Compressible Fluids on Schwarzschild Spacetime
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES

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