FIGURE 1. The initial mesh. We start the numerical test with the initial time step dt = 1/20 and with the following initial mesh (FIGURE 1). The figures (FIGURE 2,3,4,5) show the comparison between the exact and numerical velocities for the times t = 0.3, 0.5, 0.7, 1.24. Furthermore, the figures (FIGURE 6, 7) show the evolution of the corresponding meshes, which brings to light the power of the a posteriori error and corresponding bounds. FIGURE 2. t=0.3. Left: the numerical solution; right: the theoretical solution. FIGURE 3. t=0.5. Left: the numerical solution; right: the theoretical solution. FIGuRE 4. t=0.7. Left: the numerical solution; right: the theoretical solution. FIGURE 5. t=1.24. Left: the numerical solution; right: the theoretical solution. FIGURE 6. The mesh. Left : t=0.3; right : t=0.5.
