Combined DG-CG Time Stepping for Wave Equations

The continuous and discontinuous Galerkin time stepping methodologies are combined to develop approximations of second order time derivatives of arbitrary order. This eliminates the doubling of the number of variables that results when a second order problem is written as a first order system. Stability, convergence, and accuracy, of these schemes is established in the context of the wave equation. It is shown that natural interpolation of nonhomogeneous boundary data can degrade accuracy, and that this problem can be circumvented using interpolants matched with the time stepping scheme.