The finite element or finite difference techniques are well known for the solution of Maxwell's equation in differential form. But terminating the mesh accurately at a finite distance from the body in case of an open problem is a major challenge. Though there are several techniques presented before, this new method is different from the methods given in -. This new approach allows for the terminating surface to encapsulate the body very tightly. In this proposed method, finite element technique is used for open region problems whereas integral equation solution approach using Green's function is applied to enforce the radiation condition. At each iteration cycle, field sources within the domain are evaluated and their potential at the terminating surface is calculated. The proposed method leads to increased computational efficiency, of finite element method. It can be generalized for the case of inhomogeneous and nonlinear media, for static and dynamic fields. Typical numerical results are presented for the solution of Laplace's equation to illustrate the accuracy of the technique.