A Nitsche method for wave propagation problems in time domain

We propose a new Nitsche-type approach for the weak enforcement of Dirichlet and Neumann boundary conditions in the context of time-domain wave propagation problems in mixed form. A peculiar feature of the proposed method is that, due to the hyperbolic structure of the problem considered, two penalty parameters are introduced, corresponding to Dirichlet and Neumann conditions, respectively. A stability and convergence estimate is also provided, in the case of a discontinuous-in-time Galerkin space-time integrator. The spatial discretization used is based on a stabilized method with equal order interpolation for all solution components. In principle, however, the proposed methodology is not confined to stabilized methods. We conclude with an extensive set of tests to validate the robustness and accuracy of the proposed approach.