Abstract:
In this talk, we will discuss sparse grid DG methods for
computing high-dimensional PDEs. Using a hierarchical
basis representation, we construct a sparse finite
element approximation space, reducing the degree of
freedom from the standard {$O(h^{-d})$ to
$O(h^{-1}|\log_2 h|^{d-1})$} for $d$-dimensional problems,
where $h$ is the uniform mesh size in each dimension.
The accuracy of the numerical approximation of this
method is only slightly deteriorated, which is verified
by error estimates and numerical tests in multi-dimensions. |