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Two residual-type error estimators for the mortar staggered discontinuousGalerkin discretizations of second order elliptic equations are developed. Botherror estimators are proved to be reliable and efficient. Key to the derivationof the error estimator in potential $L^2$ error is the duality argument. On theother hand, an auxiliary function is defined, making it capable of decomposingthe energy error into conforming part and nonconforming part, which can becombined with the well-known Scott-Zhang local quasi-interpolation operator andthe mortar discrete formulation yields an error estimator in energy error.Importantly, our analysis for both error estimators does not require anysaturation assumptions which are often needed in the literature. Severalnumerical experiments are presented to confirm our proposed theories.

A posteriori error estimates for the mortar staggered DG method