Analytical solutions for the damped oscillations of a liquid in a parabolic container have been derived by Sampson et al [28, 17]. Figure 99 illustrates the numerical and analytical solutions at t = 1500 seconds. Wetting and drying occur at the two moving contact points and hydrostatic balance is approached as time passes.
Figure 100 gives the analytical and numerical solutions for the horizontal component of velocity (which is spatially constant). Figures 101 and 102 give the relative errors in surface elevation and horizontal velocity respectively, as functions of spatial resolution.
The errors are small and larger-than-first-order convergence rates are obtained.
Figure 100: Time evolution of the (spatially constant) horizontal velocity. Seven levels of refinement. 
