We have developed and analysed a new class of discontinuous Galerkin
methods (DG) for wave equations. The new method
can be seen as a compromise between standard DG and finite element
method
(FEM) in the way that it is
explicit as standard DG and energy conserving as FEM.
There are in the literature many methods that achieves some of the
goals
of explicit time marching, unstructured grid, energy conservation and
optimal higher order accuracy, but as far as we know only our new
algorithms satisfy all the conditions.
Stability and convergence of the new method are rigorously analysed.
The convergence rate is optimal with respect to the order of the polynomials in the finite
element spaces.
Moreover, the convergence is described by a series of numerical
experiments.
This is a joint work with Bjorn Engquist.