Interval boundary element method in the presence of uncertain boundary conditions, integration errors, and truncation errors

In engineering, most governing partial differential equations for physical systems are solved using finite element or finite difference methods. Applications of interval methods have been explored in finite element analysis to model systems with parametric uncertainties and to account for the impact of truncation error on the solutions. An alternative to the finite element method is the boundary element method. The boundary element method uses singular functions to reduce the dimension of the domain by transforming the domain variables to boundary variables. In this work, interval methods are developed to enhance the boundary element method for considering causes of imprecision such as uncertain boundary conditions, truncation error, and integration error. Examples are presented to illustrate the effectiveness and potential of an interval approach in the boundary element method.