Robust Local Flux Reconstruction for Various Finite Element Methods

We present a uniform approach to local reconstructions of the gradient of primal approximations by conforming, nonconforming and totally discontinuous finite elements of arbitrary order. We start from a hybrid formulation which covers all considered methods and whose Lagrange multipliers approximate the normal fluxes. It turns out that the multipliers can be computed locally and are next used to define local corrections of the flux. We also show that the DG solution and reconstructed flux with stabilisation parameter γ converge uniformly in h with the convergence rate 1∕γ towards the CG or NC ones, depending on the stabilisation.