Abstract
Hyperbolic conservation laws arise in the context of continuum physics, and are mathematically presented in differential form and understood in the distributional (weak) sense. The formal application of the Gauss-Green theorem results in integral balance laws, in which the concept of flux plays a central role. This paper addresses the spacetime viewpoint of the flux regularity, providing a rigorous treatment of integral balance laws. The established Lipschitz regularity of fluxes (over time intervals) leads to a consistent flux approximation. Thus, fully discrete finite volume schemes of high order may be consistently justified with reference to the spacetime integral balance laws.
Original language | English |
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Pages (from-to) | 2048-2063 |
Number of pages | 16 |
Journal | Communications on Applied Mathematics and Computation |
Volume | 6 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2024 |
Bibliographical note
Publisher Copyright:© Shanghai University 2023.
Keywords
- Balance laws
- Consistency
- Finite volume approximations
- Flux regularity
- Hyperbolic conservation laws
- Primary 35L65
- Secondary 76M12 · 65M08