Absorbing Boundary Conditions for Hyperbolic Systems
Matthias Ehrhardt 1*1 Lehrstuhl fur Angewandte Mathematik und Numerische Analysis, Fachbereich C Mathematik und Naturwissenschaften, Bergische Universitat Wuppertal, Gausstrasse 20, 42119 Wuppertal, Germany.
Received 13 January 2010; Accepted (in revised version) 13 January 2010
This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.AMS subject classifications: 65M06, 35L50
Key words: Absorbing boundary conditions, hyperbolic system, Engquist and Majda approach, strict well-posedness, GKS-stability.
Email: firstname.lastname@example.org (M. Ehrhardt)