A complex variable boundary element method for solving a steady-state advection-diffusion-reaction equation

An accurate complex variable boundary element method is proposed for the numerical solution of two-dimensional boundary value problems governed by a steady-state advection-diffusion-reaction equation. With the aid of the Cauchy integral formulae, the task of constructing a complex function which gives the solution of the boundary value problem under consideration is reduced to solving a system of linear algebraic equations. The method is applied to solve several specific problems which have exact solutions in closed form and a problem of practical interest in engineering.