Weak boundary conditions for wave propagation problems in confined domains: Formulation and implementation using a variational multiscale method

We propose a new approach to the enforcement of Dirichlet, Neumann, or Robin boundary conditions in finite element computations of wave propagation problems. The key idea is to enforce the boundary conditions weakly as part of the variational formulation. Due to the hyperbolic structure of the problem considered, the variational formulation does not require any penalty parameters, in contrast with what typically happens in elliptic or advection-diffusion (parabolic) problems. This article presents the implementation of the proposed boundary condition framework using a variational multiscale method for the wave equation in mixed form. We conclude with an extensive set of tests to validate the robustness and accuracy of the proposed approach.