An Efficient Framework for Using Higher-Order Curved Div-Conforming Elements With Cancellation of Weak Singularities in Local Space for Surface Integral Equation

A reliable scheme for using higher-order curved div-conforming elements is presented. This procedure takes advantage of tangential basis functions developed for finite-element applications. Throughout the theorem of trace, the Helmholtz decomposition into solenoidal and nonsolenoidal subspaces is converted into a Hodge decomposition for the surface currents. Furthermore, a cancellation of the singular term appearing within the integrals is carried out acting in the local space, avoiding the difficulties associated to the curved domains, when coordinate transformations are used with this propose.