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

Dus Mathias (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 [11] and a careful use of Harten formalism.

Mots clés: Exponential stability; bounded variation; scalar conservation laws; flux limiter scheme

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Dus Mathias. Exponential stability of a general slope limiter scheme for scalar conservation laws subject to a dissipative boundary condition. Mathematics of Control, Signals, and Systems, 2021. ⟨hal-03398730⟩