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May 3, 2026

On the Consistency and Convergence Theory of the Godunov–Roe Method for Systems of Balance Laws

Key Points

The aim is to analyze the convergence and consistency of the Godunov–Roe method for hyperbolic systems with source terms.
Introduced families of paths to define weak solutions in a nonconservative framework.
Analyzed the relation between weak solutions and Roe-type schemes.
Established uniform bounds on the total variation of numerical solutions under C.F.L and monotonicity conditions.
Proved convergence of the Roe scheme to a weak solution per the Dal Maso–LeFloch–Murat theory.
Demonstrated that the schemes maintain uniform bounds on total variation in specified conditions.

Abstract

ABSTRACT We study the convergence and consistency of the Godunov–Roe method for hyperbolic systems of balance laws with source terms depending on a piecewise constant function. By introducing appropriate families of paths, we define weak solutions in the nonconservative framework and analyze their relation to Roe‐type schemes. We establish uniform bounds on the total variation of the numerical solutions under the C.F.L and monotonicity conditions. Furthermore, we prove convergence of the Roe scheme to a weak solution in the sense of Dal Maso–LeFloch–Murat.

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Authors

Duong Xuan Vinh

Nguyen T. D. Huong

Journals

Numerical Methods for Partial Differential Equations

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Institutions

Ho Chi Minh City University of Science

FPT University

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Building similarity graph...

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On the Consistency and Convergence Theory of the Godunov–Roe Method for Systems of Balance Laws

Key Points

Abstract

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Connected Papers

Discussion

Authors

Journals

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Institutions

References and Citations

Citation Network

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