Numerical Analysis of the Jacobi Spectral Collocation Method for High‐Dimensional Volume‐Constrained Nonlocal Models With Weakly Singular Kernels

In this article, the numerical analysis of the Jacobi spectral collocation method for high‐dimensional volume‐constrained nonlocal models with weakly singular kernels is established. A rigorous convergence analysis has been established to show that the approximate solution of the method can achieve spectral accuracy for sufficiently smooth solutions in the sense of norm. Moreover, the asymptotically compatible property of the numerical method has been proved, that is, we show that the numerical solution can converge to its correct local limit as nonlocal interactions vanish. Finally, some numerical examples are shown to support the convergence analysis.