An adaptive high-order piecewise polynomial based sparse grid collocation method with applications

This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The is a popular technique for high dimensional problems, and the associated has been well studied in literature. contribution of this work introduction systematic framework high-order space that allowed to be discontinuous. We consider both Lagrange Hermite interpolation methods on nested points. Our construction includes wide range function space, including those used continuous finite element method. Error estimates are provided, numerical results interpolation, integration some benchmark problems uncertainty quantification compare different schemes.