  We compute the waves propagating on the compact surface of constant negative
curvature and genus 2. We adopt a variational approach using finite elements.
We have to implement the action of the fuchsian group by suitable boundary
conditions of periodic type. A spectral analysis of the wave allows to compute
the first eigenvalues of the Laplace-Beltrami operator. We test the exponential
decay due to a localized dumping and the ergodicity of the geodesic flow.
