A conforming DG method for linear nonlocal models with integrable kernels
Provides an efficient numerical method for nonlocal problems in mechanics and diffusion, with proven asymptotic compatibility.
The authors develop a new discontinuous Galerkin method for solving nonlocal constrained value problems with integrable kernels, achieving optimal convergence rates in 1D and near-optimal in 2D under weak assumptions.
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.