Complex Variable Boundary Element Method Error Analysis Using Taylor Series

Abstract

The CVBEM is a numerical approach to solving boundary value problems of two-dimensional Laplace and Poisson equations. The CVBEM estimator exactly solves the governing partial differential equations in the problem domain, but only approximately satisfies the problem boundary conditions. In this paper, a new CVBEM error measure is used in aiding in the development of improved CVBEM approximators. The new approach utilizes Taylor series theory, and can be readily programmed into computer software form. Based on numerous test applications, it appears that use of this new CVBEM error measure leads to the development of significantly improved CVBEM approximation functions.