Abstract: The finite element method is combined with the natural boundary element method to study the weak solvability and Galerkin approximations of a class of semilinear exterior boundary value problems.Theoretical analysis is mainly based on the variational formulation with constraints.The error estimate of the finite element solution and the asymptotic rate of convergence O(hⁿ) are obtained.Finally,a numerical example is devoted to illustrate this new method.

Key words: finite element method, natural boundary element method, Galerkin approximation, numerical method