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

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.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE