Convergence and error estimates of relaxation schemes for multidimensional conservation laws

DOI10.1080/03605309908821429zbMath0926.35088OpenAlexW2066538206WikidataQ60149149 ScholiaQ60149149MaRDI QIDQ4242977

Markos A. Katsoulakis, Georgios T. Kossioris, Charalambos G. Makridakis

Publication date: 29 November 1999

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309908821429

zbMATH Keywords

Kruzhkov entropy conditionssemidiscrete and fully relaxation schemes

Mathematics Subject Classification ID

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

Related Items (10)

Stringent error estimates for one-dimensional, space-dependent \(2\times 2\) relaxation systems ⋮ Transient \(L^1\) error estimates for well-balanced schemes on non-resonant scalar balance laws ⋮ A relaxation scheme for conservation laws with a discontinuous coefficient ⋮ Finite volume relaxation schemes for multidimensional conservation laws ⋮ Convergence of relaxation schemes to the equations of elastodynamics ⋮ Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws ⋮ Numerical solution of the two-dimensional shallow water equations by the application of relaxation methods ⋮ Time-Splitting Schemes and Measure Source Terms for a Quasilinear Relaxing System ⋮ A review of a posteriori error control and adaptivity for approximations of non‐linear conservation laws ⋮ The third-order relaxation schemes for hyperbolic conservation laws

Cites Work

• Unnamed Item
• Hyperbolic conservation laws with relaxation
• Measure-valued solutions to conservation laws
• A study of numerical methods for hyperbolic conservation laws with stiff source terms
• A system of conservation laws including a stiff relaxation term; the 2D case
• Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation
• Kruzkov’s estimates for scalar conservation laws revisited
• Convergence of relaxation schemes for conservation laws
• Contractive relaxation systems and the scalar multidimensional conservation law
• A MUSCL method satisfying all the numerical entropy inequalities
• The relaxation schemes for systems of conservation laws in arbitrary space dimensions
• A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach
• Error Estimates for Finite Element Methods for Scalar Conservation Laws
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES

This page was built for publication: Convergence and error estimates of relaxation schemes for multidimensional conservation laws