Comparison of continuous and discontinuous elements in boundary element method for heat transfer problems with non-linear boundary conditions

Abstract

Boundary element method (BEM) is a numerical method for solving partial differential equations. The major benefit of BEM is to reduce the dimensionality from volumes (3D problems) to surfaces or from surfaces (2D problems) to contours through the discretization of the boundary only. BEM results in high-accuracy approximations in linear problems such as Laplace equation. The main reason for such high accuracy is that the BEM employs fundamental solutions that are mainly analytical solutions of the infinite problem. In this study, the main aim is to solve 2-D conduction heat transfer with non-linear boundary conditions in a quarter hollow cylinder with different discretization schemes. Discretizations with both continuous and discontinuous parametric shape functions with different degrees of Lagrangian polynomials are performed, and the accuracy of different discretization schemes is assessed.