A new Glimm functional and convergence rate of Glimm scheme for general systems of hyperbolic conservation laws

DOI10.1007/s00205-009-0266-1zbMath1194.65104OpenAlexW2071879242MaRDI QIDQ982298

Tong Yang, Jiale Hua, Zaihong Jiang

Publication date: 6 July 2010

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-009-0266-1

zbMATH Keywords

convergencefinite difference methodGlimm functionalGlimm schemesystems of hyperbolic conservation laws

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items

On a quadratic functional for scalar conservation laws ⋮ Decay estimation in nonlinear hyperbolic system of conservation laws ⋮ Sharp convergence rate of the Glimm scheme for general nonlinear hyperbolic systems ⋮ A new nonlinear functional for general scalar conservation laws ⋮ Quadratic interaction functional for general systems of conservation laws

Cites Work

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• On the Riemann problem for non-conservative hyperbolic systems
• \(L^1\) stability estimates for \(n\times n\) conservation laws
• The semigroup generated by \(2 \times 2\) conservation laws
• Vanishing viscosity solutions of nonlinear hyperbolic systems
• Hyperbolic systems of conservation laws II
• Admissible solutions of hyperbolic conservation laws
• Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation
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• Well-posedness of the Cauchy problem for 𝑛×𝑛 systems of conservation laws
• On the convergence rate of vanishing viscosity approximations
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• The Sharpness of Kuznetsov's O(√Δx)L 1 -Error Estimate for Monotone Difference Schemes
• Solutions in the large for nonlinear hyperbolic systems of equations
• Decay of solutions of systems of nonlinear hyperbolic conservation laws
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