An Explicit A Priori Estimate for a Finite Volume Approximation of Linear Advection on Non-Cartesian Grids

We propose an elementary proof of strong convergence for a finite volume approximation of nonstationary linear advection on arbitrary grids in two space dimensions. This proof is elementary in the sense that the basic a priori estimate uses only some discrete integrations by parts and the Cauchy--Schwarz inequality. Numerical results show that the estimate is probably nonoptimal.

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