Adaptive strategies based on equilibration for the Biot equations

The hypercircle theorem leads to a posteriori error estimates for the three-field variational formulation of Biot problem involving displacements, total pressure and fluid pressure. Based thereon, adaptive strategies can be constructed. In particular, estimator is derived on basis Hdiv-conforming reconstructions stress flux approximations while symmetry reconstructed allowed satisfied only weakly. therefore performed locally set vertex patches. local nature reconstruction two different possible strategies. this paper, we review these problem. Numerical experiments underline differences between