AN ADAPTIVE LEAST-SQUARES FEM FOR LINEAR ELASTICITY WITH OPTIMAL CONVERGENCE RATES

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. The point is robustness in the sense that the crucial input parameters Theta for the Dorfler marking and kappa for the separate marking as well as the equivalence constants in the asymptotic convergence rates do not degenerate as the Lame parameter lambda tends to infinity.