Neumann Boundary Value Problems with BEM and Collocation

Abstract

This paper is an introduction into the Boundary Element Method (BEM) with collocation to find the numerical solution of two different types of Neumann problems. At first we start with the Laplace equation and continue later with the heat equation on a bounded convex domain with smooth boundary in two dimensions. We will show how to transform the governing problem into a boundary integral equation which can be solved by dividing the boundary into a finite number of segments and applying the collocation method. We finish presenting an example of the heat equation.