On the numerical solution of diffusion-reaction equations with singular source terms

A numerical study is presented of reaction-diffusion problems having singular reaction source terms, singular in the sense that within the spatial domain the source is defined by a Dirac delta function expression on a lower dimensional surface. A consequence is that solutions will be continuous, but not continuously differentiable. This lack of smoothness and the lower dimensional surface forms an obstacle for numerical discretization, including amongst others order reduction. In this paper the finite volume approach is studied for linear and nonlinear test models. The aimed application field lies in developmental biology from which a test model is used for numerical illustration