Comparison of Clenshaw–Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs

F. Nobile, L. Tamellini, R. Tempone

Uncertainty Quantification ; PDEs with random data ; linear elliptic equations ; Stochastic Collocation methods ; Sparse grids approximation ; Leja points ; Clenshaw–Curtis points

2015

In this work we compare numerically different families of nested quadrature points, i.e. the classic Clenshaw–Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence suggests that the performances of both families are essentially comparable within such framework.