| |
ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
|
Material Type |
Article
|
Author(s) |
COHEN, ALBERT (Author)
DEVORE, RONALD (Author)
|
Source Journal Info. |
Title:
Analysis and Applications
|
|
Volume/ Issue No.: 2011/JAN V.9 N.1
Call No.:515.05 AAP Location: Periodicals & References Hall - 2nd floor
|
Physical Description |
p 11-48
|
Subject Area/ Descriptors |
Mathematics
(2980)
|
|
|
Abstract |
Parametric partial differential equations are commonly used to model physical systems. They also arise when Wiener chaos expansions are used as an alternative to Monte Carlo when solving stochastic elliptic problems. This paper considers a model class of second order, linear, parametric, elliptic PDE's in a bounded domain D with coefficients depending on possibly countably many parameters. It shows that the dependence of the solution on the parameters in the diffusion coefficient is analytically smooth. This analyticity is then exploited to prove that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations can be simultaneously approximated by multivariate polynomials (in the parameters) with coefficients...
Full Abstract
|
| More Articles from:
Journal:
Analysis and Applications
(231)
Issu: 2011/JAN V.9 N.1
|
|
|
|
| |
|
Search Through eResources |
● |
● |
Related topics |
|
|
|
|