Discontinuous Galerkin for the wave equation: a simplified a priori error analysis

Figures & data

Figure 1. Temporal rate of convergence with uniform in time $L^2$-norm for the displacement and the velocity, with T = 1, 10: (left) dG(0) (right) dG(1).

Figure 2. Behaviour of the errors $\Vert e_1\left(t\right)\Vert$ and $\Vert e_2\left(t\right)\Vert$ in time: (up) dG(0) (down) dG(1).

Figure 3. Comparison of the theoretical (continuous) energy and the discrete energy for different values of the time step k: (left) dG(0) (right) dG(1).

Figure 4. Discrete energy: (left) dG(0) with $k=10\cdot 2^{-9}$ (right) dG(1) with $k=10\cdot 2^{-7}$.