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For elliptic interface problems, this paper studies residual-based aposteriori error estimations for various finite element approximations. For theconforming and the Raviart-Thomas mixed elements in two-dimension and for theCrouzeix-Raviart nonconforming and the discontinuous Galerkin elements in bothtwo- and three-dimensions, the global reliability bounds are established withconstants independent of the jump of the diffusion coefficient. Moreover, weobtain these estimates with no assumption on the distribution of the diffusioncoefficient.

Finite Element Methods for Interface Problems: Robust Residual-Based A Posteriori Error Estimates