Solution of 3D-Laplace and Helmholtz equations in exterior domains using hp-infinite elements Original Research Article

This work is devoted to a convergence study for infinite element discretizations for Laplace and Helmholtz equations in exterior domains. The proposed approximation applies to separable geometries only, combining an hp FE discretization on the boundary of the domain with a spectral-like representation (resulting from the separation of variables) in the ‘radial’ direction. The presentation includes a convergence proof for the Laplace equation and a stability analysis for the variational formulation of the Helmholtz equation in weighted Sobolev spaces. The theoretical investigations are verified and illustrated with numerical examples for the exterior spherical domain.