On the Analysis of Finite Volume Methods for Evolutionary Problems

Finite volume or finite element methods now dominate the modeling of steady flows because of their natural handling of complex configurations. They should have a similar advantage for unsteady flows; however, their error analysis on nonuniform meshes has met a number of difficulties. In this paper a new approach is adopted which makes greater use of a Godunov formulation. It opens the way for a fuller comparison of characteristic-based methods with semidiscrete methods.