Modeling, analysis, computation and application of kinetic equations

Sparse grid discontinuous Galerkin schemes for high-dimensional PDEs

Yingda Cheng

Michigan State University

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.