SIAM Journal on Scientific and Statistical Computing
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
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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 form an obstacle for numerical discretization, including amongst others order reduction. In this paper the standard finite volume approach is studied for which reduction from order two to order one occurs. A local grid refinement technique is discussed which overcomes the reduction.