Consideration of a CVBEM approximation for plane hydrodynamics

The complex variable boundary element method (CVBEM) represents a very useful working tool for applied mathematics in general and for hydrodynamics in particular. The goal of the present work is to give a brief survey on some approximation procedures given the data on the working domain contour in view of getting a rapid convergence of the whole process within a CVBEM. In the first section of this work we will see how some important mixed boundary value problems, for simply connected domains and for the Laplace operator, are transformed into equivalent Dirichlet problems and consequently these Dirichlet problems are the only boundary value problems we will deal with for a CVBEM. In the second section of the present work, some convergent algorithms of a CVBEM, for a Dirichlet boundary problem are built up in view of fluid dynamics (but not only!) applications.