Two a posteriori error estimates for one-dimensional scalar conservation laws

In this paper, we propose a posteriori local error estimates for numerical schemes in the context of one-dimensional scalar conservation laws. We rst consider the schemes for which a consistent in-cell entropy inequality can be derived. Then we extend this result to second-order schemes written in v iscous form satisfying weak entropy inequalities. As an illustration, we sh ow several numerical tests on the Burgers equation and we propose an adapti ve algorithm for the selection of the mesh.