eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2017-03-30 5 1 14 21 10.12691/ajams-5-1-4 AJAMS2017514 article Hassan Ghassemi gasemi@aut.ac.ir 1 Alireza Ahani 1 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran This paper deals with solving the quantity element using new numerical techniques on discontinues boundary element method (DBEM). The common practice in getting solution with BEM is using constant element and for that, in a Sub-parametric element, quantity has a constant value along the element and geometry discretization is supposed to have a linear variation. But using higher order (polynomial) distribution of quantity over elements could have a better description of physical process. For this, the corresponding discretized expressions based on new techniques are derived and used for solution of Laplace equation. Many results for the quantity elements are presented and discussed for the ellipse at various diameters and mesh numbers. http://pubs.sciepub.com/ajams/5/1/4/ajams-5-1-4.pdf boundary element method linear element discontinuous element