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Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Adaptive mesh-refining is of particular importance in computational mechanics and established here for the lowest-order locking-free least-squares finite element scheme which solely employs conforming $P_1$ approximations for the displacement and lowest-order Raviart--Thomas approximations for the stress variables. This forms a competitive discretization in particular in three-dimensional linear elasticity with traction boundary conditions although the stress approximation does not satisfy the symmetry condition exactly. The paper introduces an adaptive mesh-refining algorithm based on separate marking and exact solve with some novel explicit a posteriori error estimator and proves optimal convergence rates. 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