Seminar series
Date
Tue, 21 May 2024
Time
14:00 -
14:30
Location
L1
Speaker
Thomas Round
Organisation
Birmingham University
Finite element methods are often used to compute approximations to solutions of problems involving partial differential equations (PDEs). More recently, various techniques involving finite element methods have been utilised to solve PDE problems with parametric or uncertain inputs. One such technique is the stochastic collocation finite element method, a sampling based approach which yields approximations that are represented by a finite series expansion in terms of a parameter-dependent polynomial basis.
In this talk we address the topic of goal-oriented strategies in the context of the stochastic collocation finite element method. These strategies are used to approximate quantities of interest associated with solutions to PDEs with parameter dependent inputs. We use existing ideas to estimate approximation errors for the corresponding primal and dual problems and utilise products of these estimates in an adaptive algorithm for approximating quantities of interest. We further demonstrate the utility of the proposed algorithm using numerical examples. These examples include problems involving affine and non-affine diffusion coefficients, as well as linear and non-linear quantities of interest.