Before revision:  Moreover, a provably efficient local design of the equilibrated fluxes is presented that reduces the numerical costsof the error estimator. All theoretical findings are verified by numerical examples which also show that the efficiency indices of our novel guaranteed upper bounds for the velocity error are close to 1.
After revision:  Moreover, a provably efficient local design of the equilibrated fluxes with comparably low numerical costs. Numerical examples verify the theoretical findings and show that efficiency indices of our novel guaranteed upper bounds for the velocity error are close to 1.