Coupling Finite Difference Methods and Integral Formulas for Elliptic Problems Arising in Fluid Mechanics

This article is devoted to the numerical analysis of two classes of iterative methods that combine integral formulas with finite-difference Poisson solvers for the solution of elliptic problems. The first method is in the spirit of the Schwarz domain decomposition method for exterior domains. The second one is motivated by potential calculations in free boundary problems and can be viewed as a numerical analytic continuation algorithm. Numerical tests are presented that confirm the convergence properties predicted by numerica