Postprocessing of non-conservative flux for compatibility with transport in heterogeneous media

•Present an order-preserving algorithm to postprocess non-conservative fluxes on a wide range of grids.•Add a piecewise constant correction term that is minimized in a weighted L2 norm.•Application of a weighted norm appears to give better results for high contrasts in permeability.•Study both steady-state and dynamic flow models.•Solve coupled flow and transport problem to demonstrate effect of postprocessing.

A conservative flux postprocessing algorithm is presented for both steady-state and dynamic flow models. The postprocessed flux is shown to have the same convergence order as the original flux. An arbitrary flux approximation is projected into a conservative subspace by adding a piecewise constant correction that is minimized in a weighted L2 norm. The application of a weighted norm appears to yield better results for heterogeneous media than the standard L2 norm which has been considered in earlier works. We also study the effect of different flux calculations on the domain boundary. In particular we consider the continuous Galerkin finite element method for solving Darcy flow and couple it with a discontinuous Galerkin finite element method for an advective transport problem.