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An adaptive algorithm for PDE problems with random data
时间  Datetime
2017-12-14 15:00 — 16:00 
地点  Venue
Large Conference Room
报告人  Speaker
David J. Silvester
单位  Affiliation
University of Manchester
邀请人  Host
Jinglai Li
报告摘要  Abstract

We present a new adaptive algorithm for computing stochastic 
Galerkin finite element approximations for a class of elliptic PDE 
problems with random data. Specifically, we assume that the 
underlying differential operator has affine dependence on a large, 
possibly infinite, number of random parameters. Stochastic Galerkin 
approximations are then sought in the tensor product space 
$X \otimes {\cal P}$, where $X$ is a finite element space associated
with a physical domain and ${\cal P}$ is a set of multivariate polynomials 
over a finite-dimensional manifold in the (stochastic) parameter space.

Our adaptive strategy is based on computing two error estimators
(the spatial estimator and the stochastic one) that reflect the two distinct 
sources of discretisation error and, at the same time, provide effective 
estimates of the error reduction for the corresponding enhanced approximations.
In particular, our algorithm adaptively `builds' a polynomial space over a 
low-dimensional manifold in the infinitely-dimensional parameter space such 
that the discretisation error  is reduced most efficiently (in the energy norm).
Convergence of the adaptive algorithm is demonstrated numerically.

This is joint work with Alex Bespalov (University of Birmingham) and 
Catherine Powell (University of Manchester)