Stability results for the approximation of weakly coupled wave equations

Farah Abdallah (1) , Serge Nicaise (1) , Julie Valein (2, 3) , Ali Wehbe (4)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECN - Institut Élie Cartan de Nancy
4 Faculté des Sciences

In this note, we consider the approximation of two coupled wave equations with internal damping. Our goal is to damp the spurious high frequency modes by introducing numerical viscosity terms in the approximation schemes. With these viscosity terms, we show the exponential or polynomial decay of the discrete scheme when the continuous problem has such a decay (since the spectrum of the spatial operator associated with the undamped system satisfies the generalized gap condition).

Domaines: Equations aux dérivées partielles [math.AP]

Farah Abdallah, Serge Nicaise, Julie Valein, Ali Wehbe. Stability results for the approximation of weakly coupled wave equations. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2012, 350 (1-2), pp.29-34. ⟨10.1016/j.crma.2011.12.004⟩. ⟨hal-00755739⟩