We present results for all Benchmark problems using the Compact Discontinuous Galerkin (CDG) method of order 3. This method combines the stability and accuracy properties of the Local Discontinuous Galerkin (LDG) method while retaining the small stencil of other DG schemes. This reduces storage requirements and allows a simpler parallelization approach. As in the LDG method a stabilization parameter is used to penalize jumps of the discrete solution between elements. We suggest a special choice for this parameter which can be used for all test cases. The implementation is based on the DUNE software package.