An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

In this paper we consider 2D nonlocal diffusion models with a finite horizon parameter δ characterizing the range of interactions, and treatment Neumann-like boundary conditions that have proven challenging for discretizations models. We propose new generalization classical local Neumann by converting flux to correction term in model, which provides an estimate interactions each point points outside domain. While existing been shown exhibit at most first order convergence counter part as → 0, proposed Neumann-type formulation recovers case O ( 2 ) L ∞ (Ω) norm, is optimal considering equation its limit away from boundary. analyze application problem, present under solution value problem converges corresponding reduced. To demonstrate applicability condition more complicated scenarios, extend approach less regular domains, numerically verifying preserve second-order non-convex domains corners. Based on condition, develop asymptotically compatible meshfree discretization, obtaining mixed convergence.