Numerical Examples and Convergence Rates for the Multi-Element Probabilistic Collocation Method

Jasmine Foo, Brown University

The Multi-Element Probabilistic Collocation Method (MEPCM) is used to numerically approximate solution moments for PDEs with random input data. This is a natural extension of the stochastic collocation method; in the MEPCM formulation we discretize the random domain into elements and use sparse grid integration on each element. Here we will give an overview of the method and adaptivity criteria, as well as analysis of the convergence of this method under some regularity assumptions of the true solution. We will also show some numerical examples using this method on an elliptic problem with a high-dimensional random input.

Abstract Author(s): J. Foo, X. Wan, G. Karniadakis