Finite volume schemes and Lax–Wendroff consistency

Abstract

We present a (partial) historical summary of the mathematical analysis of finite difference and finite volume methods, paying special attention to the Lax–Richtmyer and Lax–Wendroff theorems. We then state a Lax–Wendroff consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates a recent generalization of the flux consistency notion designed to cope with general discrete functions.

Keywords

• Finite difference
• Lax–Wendroff consistency
• Stability
• Compactness
• Convergence