A Method of Fractional Steps for Scalar Conservation Laws without the CFL Condition

DOI10.2307/2153162zbMath0799.35150OpenAlexW4251710843MaRDI QIDQ4293964

Helge Holden, Nils Henrik Risebro

Publication date: 10 July 1994

Full work available at URL: https://doi.org/10.2307/2153162

zbMATH Keywords

Cauchy problemDafermos' method

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) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (11)

Conservation laws with a random source ⋮ Convergence Rates of the Front Tracking Method for Conservation Laws in the Wasserstein Distances ⋮ An improved front tracking method for the Euler equations ⋮ Analysis and Numerical Solvability of Backward-Forward Conservation Laws ⋮ Operator-splitting methods for the 2D convective Cahn-Hilliard equation ⋮ Unconditionally stable methods for Hamilton-Jacobi equations ⋮ A Combination of High-OrdCompact Finite Difference Schemes and a Splitting Method that Preserves Accuracy for the Multi-Dimensional Burgers' Equation ⋮ Convergence of an operator splitting method on a bounded domain for a convection-diffusion-reaction system ⋮ Three models for two phase flow in porous media ⋮ The corrected operator splitting approach applied to a nonlinear advection-diffusion problem ⋮ An unconditionally stable method for the Euler equations

Cites Work

• A numerical method for first order nonlinear scalar conservation laws in one-dimension
• The method of fractional steps for conservation laws
• Polygonal approximations of solutions of the initial value problem for a conservation law
• Global solutions of the cauchy problem for quasi‐linear first‐order equations in several space variables
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
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