# How to prove the linear convergence of the implicit euler method when applied to the semi discretised wave equation?

I'm solving the wave equation ($$u_{tt} + c^2 \Delta u = f$$) with dirichlet boundary conditions and a given starting deflection $$u_0$$ and a starting velocity $$v_0$$ in one or two dimensions. I discretised the wave equation using linear finite elements and solving it with the implicit euler method. How can I prove the first order convergence in time of this method?