eng Science and Education Publishing Applied Mathematics and Physics 2333-4886 2017-04-24 5 2 40 46 10.12691/amp-5-2-2 AMP2017522 article Milad Bamdadinejad 1 Hassan Ghassemi gasemi@aut.ac.ir 1 Mohammad Javad Ketabdari 1 Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran The purpose of the paper is to achieve relative error changes of influence coefficients based on the number of Gaussian points and relative error changes of ux and uy according to x and y using boundary element method (BEM) and constant elements. In this case, the dominant equation is Laplace's equation defined for a rectangular domain with the Dirichlet boundary condition. The boundaries of the domain will first be discretization with four constant element and four boundary conditions will be introduce in MATLAB and then four Neumann boundary conditions will be gain. Afterwards, four influence coefficients have been obtained regarding the source point within the domain and first element analytical and numerical and their relative error has been computed. Finally, ux and uy values in four points toward x and three points toward y within the domain have been computed analytical and numerical and the results have been Presented in schemes and tables. http://pubs.sciepub.com/amp/5/2/2/amp-5-2-2.pdf boundary element method laplace equation constant element influence coefficients relative error