A new posteriori error estimates for a discontinuous Galerkin method for a reaction-diffusion problem

In this paper, a new posteriori error estimates and an error indicator for locally mass conservative methods for subsurface flow are given. The methods are based on discontinuous approximation spaces, and the penalty terms on the normal fluxes across the element interfaces are added to the bilinear form to obtain the nonsymmetric interior penalty discontinuous Galerkin methods. The global explicit estimates of the error in the L2 norm are derived, and an implicit indicator of the error in the energy norm is numerically studied.