Maria Colombo, Gianluca Crippa, Marie Graff, Laura V. Spinolo
Published 2019-02-20Version 1
We deal with the numerical investigation of the local limit of nonlocal conservation laws. Previous numerical experiments suggest convergence in the local limit. However, recent analytic results state that (i) in general convergence does not hold because one can exhibit counterexamples; (ii) convergence can be recovered provided viscosity is added to both the local and the nonlocal equations. Motivated by these analytic results, we investigate the role of numerical viscosity in the numerical study of the local limit of nonlocal conservation laws. In particular, we show that the numerical viscosity of Lax-Friedrichs type schemes jeopardizes the reliability of the numerical scheme and erroneously detects convergence in cases where convergence is ruled out by analytic results. We also test Godunov type schemes, less affected by numerical viscosity, and show that in some cases they provide more reliable results.
On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes
Rate of convergence of the Nanbu particle system for hard potentials
Convergence of nodal sets in the adiabatic limit
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