We compare two algorithms to simulate the propagation, arrest, recession, and closure of a planar hydraulic fracture, focusing on their ability to capture the physical processes governing fracture recession and closure. The first algorithm is based on a fixed grid with contact detection during recession, while the second is based on a moving mesh that tracks the receding front using the appropriate receding near‐tip asymptotics. We assess the adequacy of fixed‐grid contact logic in simulating fracture recession, and evaluate the generality of the so‐called sunset solution for fracture closure, originally derived for plane‐strain and radial fractures and homogeneous properties of the elastic medium. Our comparison shows that both algorithms perform similarly for reasonable choices of fracture discretization and residual aperture parameters in the fixed‐grid case. The precision of both approaches is primarily influenced by discretization, while the minimum residual aperture parameter in the contact algorithm has a negligible effect. Using the fixed‐grid contact scheme, we also demonstrate the emergence of the sunset solution for receding hydraulic fractures under symmetry‐breaking configurations of the fracture front induced by heterogeneities, which are far beyond the constraints under which the sunset solution was originally derived.