arXiv subjects

Sanjibanee Sudha

Publications and source records attributed to Sanjibanee Sudha.

3 recordsLinked to original sources

arXiv2026

A note on the central-upwind scheme for nonlocal conservation laws

The central-upwind flux is a widely used numerical flux function for local conservation laws. It has been investigated by Kurganov and Polizzi (2009) for a specific nonlocal conservation law and can be derived from a fully-discrete second-order scheme. Here, we derive this fully-discrete scheme in detail with a particular focus on the occurring nonlocal terms. In addition, we derive the central-upwind flux for a class of nonlocal conservation laws and use an estimate on the nonlocal speed which fixes the nonlocality at the cell interfaces. We prove that the resulting first-order numerical scheme converges to the correct solution. Under additional assumptions on the analytical flux we present a similar result for a second-order central-upwind scheme. Numerical examples compare the central-upwind schemes to Godunov-type schemes and the fully-discrete scheme.

math.NA↗

arXiv2025

Convergence of the non-staggered Nessyahu-Tadmor scheme for coupled systems of one-dimensional nonlocal balance laws

We derive a second-order accurate, non-staggered central scheme based on the well-known Nessyahu-Tadmor scheme to approximate solutions of coupled systems of nonlocal balance laws. We show that the approximate solutions stay bounded by an exponential $L^\infty$ bound in time. Under linearity assumptions on the flux and source terms the approximate solutions converge weakly-$*$ to weak solutions of the nonlocal balance laws. Assuming stronger regularity, in particular on the convolution kernel, we show strong convergence towards entropy weak solutions in the nonlinear case. Numerical examples validate our results and demonstrate its applicability to various systems of nonlocal problems.

math.NA↗

arXiv2023

Numerical schemes for a class of nonlocal conservation laws: a general approach

In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then, we apply a numerical flux function on the reduced problem. We present explicit conditions which such a numerical flux function needs to fulfill. These conditions guarantee the convergence to the weak entropy solution of the considered model class. Numerical examples validate our theoretical results and demonstrate that the approach can be applied to other nonlocal problems.

math.NA↗