Martin Vohralík (Université Paris 6)

Optimal a posteriori error estimates in continuous and discontinuous Galerkin finite element and finite volume methods
We establish a posteriori error estimates on the error in continuous and discontinuous Galerkin finite element and finite volume discretizations of several model elliptic problems. Our estimates give a guaranteed upper bound (feature no undetermined constant), so that they can be used not only as indicators for adaptive mesh refinement, but also for the actual control of the error. We next discuss the question of their local efficiency, asymptotic exactness, and robustness with respect to discontinuous coefficients.