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Nonlocality is ubiquitous in nature and is a generic feature of model reduction of complex systems. Nonlocal models and nonlocal balance laws are attractive alternatives to treat anomalous processes and singular behavior. We present the framework of asymptotically compatible discretizations for parametrized variational problems associated with nonlocal models that provide convergent approximations in the nonlocal setting and in the local limit. These methods allow consistent and robust simulations of problems involving multiple scales and are helpful in the validation of nonlocal models and simulations in physical applications. | 
