Analysis of the dipole simulation method for two-dimensional Dirichlet problems in Jordan regions with analytic boundaries

This paper presents a stability and error estimate of the dipole simulation method applied to Dirichlet problems in Jordan regions. Specifically, it is proved that the error decays exponentially when the boundary data is analytic, and it decays algebraically when the boundary data is not analytic but belongs to some Sobolev space. Moreover, some numerical results and conjectures are presented.