A key problem when coordinating the behaviour of devices in situated networks (e.g., pervasive computing, smart cities, Internet of Things, wireless sensor networks) is adaptation to changes impacting network topology, density, and heterogeneity. Computational goals for such systems are often expressed in terms of geometric properties of the continuous environment in which the devices are situated, and the results of resilient computations should depend primarily on that continuous environment, rather than the particulars of how devices happen to be distributed through it. In this paper, we identify a new property of distributed algorithms, eventual consistency, which guarantees that computation selfstabilizes to a final state that approximates a predictable limit as the density and speed of devices increases. We then identify a large class of programs that are eventually consistent, building on prior results on the field calculus computational model to identify a class of self-stabilizing programs. Finally, we confirm through simulation of pervasive network scenarios that eventually consistent programs from this class can provide resilient behavior where programs that are only self-stabilizing fail badly.