Error analysis of a coupled finite–infinite element method for an exterior Poisson problem

An error estimate is presented for the numerical approximation to an exterior problem of the Poisson equation when a coupled finite–infinite element method is employed in the computation. This estimate involves not only the size h and the order p of the quasiuniform finite element approximation, but also the radius R of the computational domain covered with finite elements and the number N of the radial terms of infinite elements. Numerical tests are performed, and the results partly validate the theoretical analysis.