On the numerical solution of a model air pollution problem with non-smooth initial data
This paper considers a model air pollution problem in two space variables which can be transformed to the one-dimensional diffusion equation with a Dirac delta function as the initial condition. The primary purpose of this study is to investigate the effect of two ways of representing this highly singular initial condition, namely by L2 projection and by mollification, in commonly used numerical methods based on a Galerkin semi-discretization together with the θ method in the marching direction. Results of extensive numerical experiments are reported which demonstrate, for example, that in general the numerical solution obtained with mollified initial data is more accurate near the initial point than that obtained using projected initial data. Moreover, it is verified that the 'smoothed' Crank - Nicolson method is the most effective marching technique.
Seward, WL; Kasibhatla, PS; Fairweather, G
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