The numerical solution of nonlocal constrained value problems with integrable kernels is considered in this talk. 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 can more efficiently solve the problem numerically. The new method is shown to be asymptotically compatible. Moreover, it has optimal convergence rate for any dimensional case under mild assumptions.