The norm resolvent convergence of discrete Schrödinger operators to a continuum operator in the limit is proved under relatively weak assumptions. This result implies, particular, spectrum with respect Hausdorff distance.

We study the continuum limit for Dirac–Hodge operators defined on n dimensional square lattice $$h\mathbb {Z}^n$$ as h goes to 0. This result extends a first order discrete differential operator known convergence of Schrödinger their continuous counterpart. To be able define such analog, we start by defining an alternative framework higher–dimensional calculus. believe that this framework, gene...

We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the quasi-nonlocal quasicontinuum approximation. For simplicity, the analysis is restricted to the case of second-neighbor interactions and is linearized about a uniforml...