| Abstract: |
| We consider a class of nonlocal conservation laws modeling traffic flow, where the velocity depends on a convolution of the density with a rescaled kernel that concentrates as a parameter $\epsilon$ tends to zero. A central question is whether solutions converge to the entropy-admissible solution of the corresponding local conservation law, and how to design numerical methods that faithfully capture this transition.
We present numerical schemes that are asymptotically compatible: as the mesh size $h$ and $\epsilon$ vanish simultaneously, numerical solutions converge to the local entropy solution with an explicit rate of order $\sqrt{\epsilon}+\sqrt{h}$. We also discuss a complementary approach via compensated compactness that resolves the singular limit for rough initial data and kernels. |
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