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The error estimation scheme will be adapted to the a posteriori flux error estimate by Di Pietro and Ern.

The flux error estimate across an intersection is given by the solution jump [u_h] and the gradient jump. We extend the gradient jump to the jump in physical flux:

E_\text{flux} := C_{F, T}^{1/2} h_T^{1/2} \cdot || \overline{\omega}_F \left[ K_0 K_f \nabla_h u_h \right] \cdot \hat{\mathbf{n}}_F + \gamma \frac{\eta}{h_F} [ u_h ] ||_{L^2(\partial T)}

C_{F, T} := \left[ h_T |\partial T|_{d-1} |T|_d^{-1} \right] \left[ 2 d^{-1} + C_{P, T} \right] C_{P, T}

C_{P, T} := \pi^{-1}