LAUSR

Abstract Approximate fundamental solutions (AFS) are designed to be similar to fundamental solutions but without singularities. They have been used in the context of the Method of Fundamental Solutions and for problems of Stokes flow (where they are known as regularized stokeslets). A short survey of available AFS is given together with how they may be used to treat three-dimensional boundary-value problems for Laplace’s equations. Explicit calculations are made for a sphere, with a focus on quantifying errors. It is concluded that the use of AFS can lead to unexpectedly large errors: caution is advised when abandoning true fundamental solutions.