# A posteriori error estimates for the mortar staggered DG method

## TL;DR

This paper develops and proves the reliability and efficiency of two residual-type a posteriori error estimators for mortar staggered DG methods applied to second order elliptic equations, validated by numerical experiments.

## Contribution

It introduces two novel residual-type error estimators for mortar staggered DG methods, avoiding saturation assumptions and validated through theoretical proofs and numerical tests.

## Key findings

- Both error estimators are reliable and efficient.
- The estimators do not require saturation assumptions.
- Numerical experiments confirm the theoretical results.

## Abstract

Two residual-type error estimators for the mortar staggered discontinuous Galerkin discretizations of second order elliptic equations are developed. Both error estimators are proved to be reliable and efficient. Key to the derivation of the error estimator in potential $L^2$ error is the duality argument. On the other hand, an auxiliary function is defined, making it capable of decomposing the energy error into conforming part and 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 for both error estimators does not require any saturation assumptions which are often needed in the literature. Several numerical experiments are presented to confirm our proposed theories.