Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods

It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve Helmholtz equation in unbounded domains. In this work, applying such DtN and using finite element method, we analyze a two dimensional transmission problem describing elastic waves inside bounded closed obstacle acoustic outside it. We are mainly interested analyzing of order establish well-posedness results approximated variational equation, further derive priori error estimates involving effects both discretization truncation map. Finally, some numerical presented illustrate accuracy scheme.