Abstract
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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