Application of boundary element method on 2-D laplace equation and its error analysis

Abstract

The phenomenon of Elliptic boundary value problems is often found in everyday life, such as the problem of water infiltration in the soil, the problem of static heat conduction and the problem of wave propagation. Laplace equation is one of the elliptic equations that is mostly employed in formulating various problems in engineering studies. The analytic solution of Laplace Equation that has irregular domain and involve mixed boundary conditions is not always possible. To overcome the problem, a numerical method called Boundary Element Method (BEM) can be employed. In this study, a BEM is applied to solve the 2-D Laplace Equation. The domain considered in the study is a square shape with length and width of 1 unit. The procedures of the BEM application are basically starting with the transformation of the governing equation into boundary integral equation (BIE) followed by the discretization of the BIE to form a Linear Algebra Equation System to be solved using any available package programs. The results show that when the domain is discretised to 80 segments, the numerical solutions have the smallest error production compared to those of 20 and 40 segments.