Complex Polynomial Approximation of the LaPlace Equation

Abstract

A method of approximating the solution of the Laplace equation in two‐dimensions is presented. The numerical approach is to determine a complex variable polynomial which satisfies the specified boundary conditions along a simple closed contour. Since the method is simple to apply to time‐stepped, quasi‐steady state saturated ground water problems or moving boundary problems, a significant savings in computational effort over other boundary integral equation methods is available. Applications to a free water surface problem and a moving boundary problem are presented. Error bounds and model stability are considered.