|We consider the rotation of a scalar
with a cone as initial condition and a sharp edged bottomline:
In the following, a comparison is given
of the finite difference discretization on adaptive sparse grids and a
similar non-adaptive finite difference scheme on uniform grids.
In this example refinement is required
only near the bottom line of the cone which is a one-dimensional manifold.
Therefore, the adaptive scheme achieves twice the convergence rate (error
after one rotation vs. number of DOF) of the non-adaptive scheme.