On the Consistency of Arnoldi‐Based Krylov Methods for Conservation Laws

Abstract

AbstractConservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Re‐ cently, these concepts have been extended to the realm of iterative methods by defining locally conservative and flux consistent iterations. In this note, the current status of such iterative methods is summarized. In particular, it has been shown that Krylov subspace methods are locally conservative, but that they are not flux consistent. Here, we approach the problem of quantifying the flux inconsistency of Krylov subspace methods. Krylov methods introduce a time retardation factor into discretizations of linear conservation laws. It has thusfar been unknown how to compute the precise value of this factor. This issue is resolved herein for Arnoldi‐based Krylov subspace methods.