On the energy stability of high-order finite volume schemes for initial-boundary value problems

Abstract

We examine the energy stability of high-order finite volume schemes approximating linear hyperbolic initial- boundary value problems. In particular, we consider schemes obtained by the k-exact method and the spectral volume method using the central numerical flux. To determine the stability of the schemes we use the energy method, and investigate the resulting terms. Finally, we compute numerical results verifying the accuracy of the schemes.