# Accession Number:

## ADA522055

# Title:

## Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs

# Descriptive Note:

## Research rept.

# Corporate Author:

## TEXAS A AND M UNIV COLLEGE STATION DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 2010-05-31

# Pagination or Media Count:

## 32.0

# Abstract:

Deterministic Galerkin approximations of a class of second order elliptic PDEs with random coefficients on a bounded domain D is a subset of Rexp d are introduced and their convergence rates are estimated. The approximations are based on expansions of the random diffusion coefficients in Lexp 2D-orthogonal bases, and on viewing the coefficients of these expansions as random parameters y yomega ysub iomega. This yields an equivalent parametric deterministic PDE whose solution ux y is a function of both the space variable x is an element of D and the in general countably many parameters y. We establish new regularity theorems describing the smoothness properties of the solution u as a map from y is an element of U -1, 1exp infinity to V Hsup 1sub 0D. These results lead to analytic estimates on the V norms of the coefficients which are functions of x in a so-called generalized polynomial chaos gpc expansion of u.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics