Local discretization error bounds using interval boundary element method

In this paper, a method to account for the point‐wise discretization error in the solution for boundary element method is developed. Interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented. The developed method does not assume any special properties besides the Laplace equation being a linear elliptic partial differential equation whose Green's function for an isotropic media is known. Numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error. Copyright © 2008 John Wiley & Sons, Ltd.