An adaptive stabilized finite element scheme for a water quality model Original Research Article

Residual type a posteriori error estimators are introduced in this paper for an advection–diffusion–reaction problem with a Dirac delta source term. The error is measured in an adequately weighted image-norm. These estimators are proved to yield global upper and local lower bounds for the corresponding norms of the error. They are used to guide adaptive procedures, which are experimentally shown to lead to optimal orders of convergence.