Exponential stability of a general slope limiter scheme for scalar conservation laws subject to a dissipative boundary condition

In this paper, we establish the exponential BV stability of general systems of discretized scalar conservation laws with positive speed. The focus is on numerical approximation of such systems using a wide class of slope limiter schemes built from the upwind monotone flux. The proof is based on a Ly...

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Bibliographic Details
Published inMathematics of control, signals, and systems Vol. 34; no. 1; pp. 37 - 65
Main Author Dus, Mathias
Format Journal Article
LanguageEnglish
Published London Springer London 01.03.2022
Springer Nature B.V
Springer Verlag
Subjects
Analysis of PDEs
Banach spaces
Boundary conditions
Communications Engineering
Conservation laws
Control
Mathematics
Mathematics and Statistics
Mechatronics
Networks
Numerical Analysis
Optimization and Control
Original Article
Robotics
Slope stability
Systems Theory
Viscosity
Scalar conservation laws
Flux limiter scheme
Exponential stability
Bounded variation
bounded variation
scalar conservation laws
flux limiter scheme
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Summary:In this paper, we establish the exponential BV stability of general systems of discretized scalar conservation laws with positive speed. The focus is on numerical approximation of such systems using a wide class of slope limiter schemes built from the upwind monotone flux. The proof is based on a Lyapunov analysis taken from the continuous theory (Coron et al. in J Differ Equ 262(1):1–30, 2017) and a careful use of Harten formalism.
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ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-021-00301-2