liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity
Institute for Computational and Mathematical Engineering, Stanford University and USA, Department of Information Technology, Uppsala University, Uppsala, Sweden.
Aerospace Engineering Science Department, University of Colorado, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2013 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 258, 134-151 p.Article in journal (Refereed) Published
Abstract [en]

The stochastic Galerkin and collocation methods are used to solve an advection–diffusion equation with uncertain and spatially varying viscosity. We investigate well-posedness, monotonicity and stability for the extended system resulting from the Galerkin projection of the advection–diffusion equation onto the stochastic basis functions. High-order summation-by-parts operators and weak imposition of boundary conditions are used to prove stability of the semi-discrete system.

It is essential that the eigenvalues of the resulting viscosity matrix of the stochastic Galerkin system are positive and we investigate conditions for this to hold. When the viscosity matrix is diagonalizable, stochastic Galerkin and stochastic collocation are similar in terms of computational cost, and for some cases the accuracy is higher for stochastic Galerkin provided that monotonicity requirements are met. We also investigate the total spatial operator of the semi-discretized system and its impact on the convergence to steady-state.

Place, publisher, year, edition, pages
2013. Vol. 258, 134-151 p.
Keyword [en]
Polynomial chaos, Stochastic Galerkin, Stochastic collocation, Stability, Monotonicity, Summation-by-parts operators
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-91042DOI: 10.1016/j.cma.2013.02.009ISI: 000319180800011OAI: diva2:615896
Available from: 2013-04-19 Created: 2013-04-12 Last updated: 2013-08-30Bibliographically approved

Open Access in DiVA

fulltext(726 kB)216 downloads
File information
File name FULLTEXT01.pdfFile size 726 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Nordström, Jan
By organisation
Computational MathematicsThe Institute of Technology
In the same journal
Computer Methods in Applied Mechanics and Engineering
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 216 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 174 hits
ReferencesLink to record
Permanent link

Direct link