TITLE
Sparse adaptive polynomial chaos methods for random elliptic PDE

ABSTRACT
The solution of a partial differential equation with random
coefficients is a random field.  If the coefficients depend on a
sequence of random variables, then the solution can often be
approximated by polynomials in these random variables.  I will present
numerical methods that adaptively construct suitable spaces of
polynomials to resolve this parameter dependence.  These methods are
based on adaptive wavelet algorithms, with orthonormal polynomial
systems in place of wavelet bases.  The coefficients of the solution
with respect to these polynomials are functions on the spatial domain
and can be approximated in finite element spaces of varying size,
depending on the importance of the coefficient, in order to construct
an efficient sparse approximation of the solution.