This article analyses an inexpensive solution process for a certain classof elliptic partial differential equations with a singular solution. The modelling of singular solutions is a very frequent occurrence in the engineering modelling world. As the most common problems we can cite: the modelling of heat fluxes in domains with re-entrant corners, the modelling of inert masses attached at discrete points on plates, the modelling of stress intensity factors for crack analysis, etc. In most cases, the engineering approach to these models is to disregard the solutions around the singularity, but expect the finite-element approximation to yield acceptable results away from the singularity. If the mesh generator permits, a denser finite-element grid is generated in the vicinity of the singularity.
In this work we analyse a predefined adaptive grid pattern to better approximate the singularity in the domain. It is shown that the adaptive grid pattern not only improves the accuracy of the approximation in the vicinity of the singularity, but also the accuracy in domains away from the singularity. The technique presented also has the advantage of being easy to incorporate in existing finite-element codes.