SOLUTION OF 3D-LAPLACE AND HELMHOLTZ EQUATIONS IN EXTERIOR DOMAINS USING HP-INFINITE ELEMENTS

This work is devoted to a convergence study for infinite element discr etizations for Laplace and Helmholtz equations in exterior domains. Th e proposed approximation applies to separable geometries only, combini ng an hp FE discretization on the boundary of the domain with a spectr al-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 numerica l examples for the exterior spherical domain.