Hide menu

Polopoly will be shut down December 15, 2023. Existing pages will have to be moved before or will be removed at that date. Empolyees may read more at FAQ Polopoly Avveckling

Stochastic Galerkin Methods for Partial Differential Equations

Number of credits: 5 hp

Examiner: Jan Nordström

Course literature:

GX08: Gottlieb, Xiu, Galerkin Method for Wave Equations with Uncertain Coefficients, Commun. Comput. Phys., Vol. 3, No. 2, pp. 505-518, 2008.

PIN15: Pettersson, Iaccarino, Nordström, Polynomial Chaos Methods for Hyperbolic Partial Differential Equations, Springer, 2015.

TPME11: Tuminaro, Phipps, Miller, Elman, Assessment of Collocation and Galerkin Approaches to Linear Diffusion Equations with Random Data, International Journal for Uncertainty Quantification, Vol. 1, No. 1, pp. 19-33, 2011.

XK02: Xiu, Karniadakis, Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos, CMAME, Vol. 191, pp. 49274948, 2002.

Course contents:

Basic Concepts


Representation of random fields via spectral expansions:

PDE Theory

Reading Material: TPME11.


Linear Problems

Hyperbolic Problems

Parabolic Problems

Elliptic Problems

Reading Material: XK02, GX08


Non-intrusive Methods

Summary of the material from day 1-2

Non-intrusive methods

Reading material: TPME11


Nonlinear Problems (Burgers' equation)

Nonlinear analysis for stochastic problem guided by deterministic analysis

Analysis of the exact solution of the stochastic Burgers' equation 

Introduction to project work/assignments

Reading material: PIN15 Ch. 6


Advanced topics

Sensitivity of different PDEs

Multiple stochastic dimensions

Alternative gPC basis functions: wavelets, spatially adaptive gPC


Organisation: Lectures and exercises, mixed.

Examination: Work in small groups (or individually) on a mini project. Project topics will be provided by the lecturers. The deliverables include a report (5 pages) and mandatory homework.

Prerequisites: Basic knowledge in computational mathematics and mathematical statistics.


Course web page


Page manager: karin.johansson@liu.se
Last updated: 2022-11-14