Numer. Math. (2006) 105:193–216 DOI 10.1007/s00211-006-0041-2 Numerische Mathematik A posteriori error estimates for elliptic problems with Dirac delta source terms Rodolfo Araya · Edwin Behrens · Rodolfo Rodríguez Received: 31 August 2005 / Revised: 30 August 2006 / Published online: 25 October 2006 © Springer-Verlag 2006 Abstract The aim of this paper is to introduce residual type a posteriori error estimators for a Poisson problem with a Dirac delta source term, in L p norm and W 1,p seminorm. The 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. Mathematics Subject Classification (2000) 65N15 · 65N30 · 65N50 1 Introduction The aim of this paper is to derive an a posteriori error estimator for elliptic problems with Dirac delta source terms. This kind of problem arises in differ- ent applications as, for instance, the electric field generated by a point charge, modeling of acoustic monopoles, transport equations for effluent discharge in aquatic media, etc. R. Araya · R. Rodríguez (B ) GI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile e-mail: rodolfo@ing-mat.udec.cl R. Araya e-mail: raraya@ing-mat.udec.cl E. Behrens Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Casilla 297, Concepción, Chile e-mail: ebehrens@ucsc.cl