This paper presents a verification of an adaptive finite element algorithm for the computation of free surface flows. We use an arbitrary Lagrangian Eulerian description for the computation of the free surface. Hence, the mesh follows the deformations of the free surface. A pseudo-solid approach is used to compute the mesh deformations. Special attention must be payed to the variational formulation of the Navier-Stokes equations and to the computation of the mesh velocity to satisfy the Geometric Conservation Law (GCL). The GCL ensures that the fixed mesh order of accuracy of the time integrator is preserved on moving meshes. Thus a 3 rd order accurate implicit Runge Kutta scheme has been used. The implementation of the free surface boundary condition is then verified with the method of the manufactured solution. The solution is computed with an adaptive finite element code. An analytical solution of the free surface and Navier-Stokes equations is developed. It is used as a reference to verify the spatial and temporal convergence rates of the method. Other test cases are also presented.