| Local a posteriori error estimators are derived for linear scalar elliptic problems and the Stokes system over general polygonal domains in 2 d. The estimators lead to a sharp upper bound for the energy error in a local region of interest. This upper bound consists of H 1-type local error indicators in a slightly larger subdomain, plus weighted L2-type local error indicators outside this subdomain which account for the pollution effects. This constitutes the basis of a local adaptive refinement procedure. Numerical experiments show a superior performance than the standard global procedure as well as the generation of locally quasi-optimal meshes. |
