# A conforming DG method for linear nonlocal models with integrable kernels

## TL;DR

This paper introduces a new discontinuous Galerkin method for solving linear nonlocal models with integrable kernels, achieving optimal convergence in 1D and near-optimal in 2D, ensuring efficiency and accuracy.

## Contribution

It proposes a novel conforming DG method tailored for nonlocal problems with integrable kernels, demonstrating asymptotic compatibility and optimal convergence rates.

## Key findings

- Method is asymptotically compatible.
- Achieves optimal convergence in 1D.
- Attains nearly optimal convergence in 2D.

## Abstract

Numerical solution of nonlocal constrained value problems with integrable kernels are considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The structure of the true solution to the problem is analyzed first. The analysis leads naturally to a new kind of discontinuous Galerkin method that efficiently solve the problem numerically. This method is shown to be asymptotically compatible. Moreover, it has optimal convergence rate for one dimensional case under very weak assumptions, and almost optimal convergence rate for two dimensional case under mild assumptions.