Variational multiscale a posteriori error estimation for systems. Application to linear elasticity

•An explicit residual-based error estimator is proposed for linear elasticity.•The constants of the method are derived from the variational multiscale theory.•Fine-scale Green’s function tensor has been explicitly computed.•Attained global and local efficiencies are satisfactory in the H1 semi-norm.•The error estimate involves little computational effort and it is easy to implement.

This paper presents an explicit   residual-based a posteriori error estimator for linear elasticity. The method is derived from the variational multiscale theory, where the subgrid scales and the constants of the method are calculated explicitly from fine-scale Green’s functions. Several numerical examples are presented, showing satisfactory local and global efficiencies when the H1H1-seminorm is employed. The formulation, which is applied to plane stress problems, can be easily extended to other elasticity problems.