State-of-the-art numerical techniques for solving partial differential equations utilize adaptive grid techniques. In these methods, the mesh is refined based on a posteriori error estimates. However, these techniques have not been used for air pollution simulations since software is available only for certain limiting forms of equations. The aim of this study is to identify parameters that affect the accuracy of numerical solutions of the transport equations involving point sources. Based on these, a grid can be chosen a priori and used for the entire simulation. A two-dimensional finite element model using bilinear elements is presented for the advection-diffusion problem with an infinite line source. This paper is restricted to two spatial directions, with advection dominating in the x-direction and turbulent diffusion dominating in the z-direction. Numerical results for an inert plume emanating from a single infinite line source show that the ratio of the advection time scale to the turbulent diffusion time scale, KzΔx uΔz2, should be equal to or greater than one for the most accurate solutions. In addition, comparisons between the volume-averaged representation of a point source and the use of an irregular grid for point source representation demonstrate that, near the source, improved results can be obtained by placing a node at the source location. © 1988.