A Posteriori error estimates for a discontinuous galerkin method applied to elliptic problems. Log number: R74

A posteriori error estimates for locally mass conservative methods for subsurface flow are presented. These methods are based on discontinuous approximation spaces and referred to as discontinuous Galerkin methods. In the case where penalty terms are added to the bilinear form, one obtains the nonsymmetric interior penalty Galerkin methods. In a previous work, we proved optimal rates of convergence of the methods applied to elliptic problems. Here, h adaptivity is investigated for flow problems in 2D. We derive global explicit estimators of the error in the L2 norm and we numerically investigate an implicit indicator of the error in the energy norm. Model problems with discontinuous coefficients are considered.