A POSTERIORI ERROR ESTIMATES FOR THE MORTAR STAGGERED DG METHOD

. Residual-type error estimators in energy error for the mortar staggered discontinuous Galerkin (DG) discretizations of second order elliptic equations were developed. The error estimator was proved to be reliable and efficient. An auxiliary function was defined, making it capable of decomposing the energy error into a conforming part and a nonconforming part, which can be combined with the well-known Scott-Zhang local quasi-interpolation operator, and the mortar discrete formulation yields an error estimator in energy error. Importantly, our analysis does not require any saturation assumptions, which are often needed in the literature. Several numerical experiments were presented to confirm our proposed theories.