Entrance hall of the ICMS Workshop

Numerical Analysis of Stochastic PDEs

May 11, 2009 - May 12, 2009

14 India Street, Edinburgh EH3 6EZ


Name Institution
Buckwar, Evelyn Heriot-Watt University
Lord, Gabriel Heriot-Watt University

Short report

The numerical solution of stochastic PDEs (SPDEs) is a very active area of research and is of both theoretical and practical interest. Quoting from the feedback summary of the participants: The key future research direction in my field is exactly Numerics for SPDEs. and In connection with the solution of differential equations with random data I see the key future research directions in more effective and accurate methods under simpler and more realistic assumptions on the data. Furthermore the modeling problem seems to me to become more important.
The topics of the talks thus covered a range of aspects of numerical analysis and applications of SPDEs. In particular there were talks treating different types of SPDEs, e.g., Allen-Cahn equation with additive noise, the stochastic wave equation and the stochastic Landau-Lifschitz equation, as well as random PDEs; different numerical schemes and convergence notions, e.g., exponential integrators, Itô-Taylor expansions or splitting schemes for Monte-Carlo methods or pathwise approximation; different types of application area, e.g., groundwater or multiphase flow, ferromagnetism and stochastic diffusive interfaces. The participants commented very favourably on the breadth of topics. The meeting was attended by 30 participants, established researchers from various backgrounds, as well as PhD students. The goals of the meeting were met and, quoting from the feedback form again: By my opinion the academic value was very high, the researchers gave impressive talks about their very recent work.

Download the full report here.


Introduction to workshop

In this meeting we aim to bring together researchers focusing on the analysis of stochastic partial differential equations (SPDEs), those concentrating on the applications and researchers designing and analysing numerical schemes for SPDEs. Such a three way interaction is the key to designing efficient and accurate numerical schemes as well as a good understanding of the physical processes and can assist and open new avenues in the mathematical analysis.

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You may register your interest in attending this meeting by completing the application form, which is available at the top of this page. You will receive an e-mail indicating whether you have been allocated a place. Speakers will receive a separate invitation via e-mail.

If you do not receive an e-mail please contact Irene Moore.

The workshop will take place at the head-quarters of ICMS, 14 India Street, Edinburgh. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, near the city centre.

The ICMS travel pages contain advice on how to travel to Edinburgh. For local information the finding ICMS page shows the location of ICMS and contains useful maps of the city centre.

The seminar room at ICMS has four whiteboards, two overhead projectors, a data projector and laptop.

Wireless access is available throughout the ICMS building. There are also three public PCs which may be used at any time for internet access and to check email.

Participants should make their own accommodation arrangements: it will be possible to reclaim part of these costs through ICMS. Further details will be provided in early April. A list of Edinburgh accommodation of various sorts and prices is available here . Sections 1-3 are particularly relevant.

Invited participants should refer to their personal invitation letter for accommodation arrangements.

Meals and Refreshments
A buffet lunch will be provided on the Monday 11 and Tuesday 12 May.

Morning and afternoon refreshments will be provided throughout the workshop.

There will be an informal wine reception and poster session after the close of lectures on Monday 11 May, followed by a workshop dinner.

Poster Session
A poster session will take place after the close of lectures on Monday 11 May. The number of posters will be limited to 10 and size to A1 Portrait, due to space restrictions. Please indicate on your application form if you are interested in presenting a poster.

Registration will take place on Monday 11 May at 09.00.

Financial Arrangements
Unless otherwise specified in your invitation letter, the workshop grant will cover tea/coffee throughout the workshop, lunch on both days, the wine reception and the workshop dinner. It will also be possible for participants to claim a contribution towards travel, accommodation and local expenses. This contribution will be confirmed soon.

Reimbursement will take place after the workshop. At Registration you will be given an expenses claim form that should be submitted to ICMS, with receipts. Your expenses will be paid directly into your bank account so you will need to provide your account details plus IBAN, SWIFT or Routing numbers as applicable. Please note that we cannot reimburse any item without a receipt.



Monday 11 May

09.00 - 10.00
10.00 - 10.45
Tony Shardlaw (University of Manchester)
Pathwise error bounds for exponential integrator scheme
10.45 - 11.15
11.15 - 12.00
Omar Lakkis (University of Sussex)
Computations and Stochastic Diffuse-Interface Models
12.00 - 12.45
Istvan Gyongy (University of Edinburgh)
Accelerated finite difference schemes
12.45 - 14.00
14.00 - 14.45
Patrick Jenny (ETH Zürich)
Stochastic modelling of non-equilibrium multi-phase flow to link pore scale dynamics with Darcy scale behaviour
14.45 - 15.30
Rob Scheichl (University of Bath)
Computational challenges in Uncertainty Quantification
15.30 - 16.00
16.00 - 16.45
Wolfgang Nowak (Institut für Wasserbau)
Challenges and Demands from the Application Side of Stochastic Modelling
16.45 - 17.30
Erika Hausenblas (University of Salzburg)
The Numerical Approximation of the Stochastic Wave equation
17.30 - 18.30
Wine reception 


Tuesday 12 May

09.00 - 09.45
Rachel Kuske (University of British Columbia)
Competition of different noise sources in delay dynamics
09.45 - 10.30
Arnulf Jentzen (Johann Wolfgang Goethe-University)
Higher order numerical approximation of stochastic partial differential equations - a Taylor expansion approach
10.30 - 11.00
11.00 - 11.45
Nicolai Krylov (University of Minnesota)
On the It^o and It^o-Wentzell formulas in the theory of SPDEs
11.45 - 12.30
Zdzislaw Brzezniak (University of York)
On stochastic PDEs and ferromagnetism
12.45 - 14.00


Presentation Details
Brzezniak, Zdzislaw
On stochastic PDEs and ferromagnetism
View Abstract Down
Gyongy, Istvan
Accelerated finite difference schemes
View Abstract Down
Hausenblas, Erika
The numerical approximation of the stochastic wave equation
View Abstract Down
Jenny, Patrick
Stochastic modeling of non-equilibrium multi-phase flow to link pore scale dynamics with Darcy scale behaviour
View Abstract Down
Jentzen, Arnulf
Higher order numerical approximation of stochastic partial differential equations - a Taylor expansion approach
View Abstract Down
Krylov, Nicolai
On the It^o and It^o-Wentzell formulas in the theory of SPDEs
View Abstract Down
Kuske, Rachel
Competition of different noise sources in delay dynamics
View Abstract Down
Lakkis, Omar
Computing the stochastic Allen-Cahn problem
View Abstract Down
Nowak, Wolfgang
Challenges and demands from the application side of stochastic modelling
View Abstract Down
Scheichl, Rob
Computational challenges in Uncertainty Quantification
View Abstract Down
Shardlow, Tony
Pathwise error bounds for exponential integrator scheme
View Abstract Down


Name Institution
Banas, Lubomir University of Bielefeld, Germany
Bocharov, Boris University of Edinburgh
Brzezniak, Zdzislaw University of York
Buckwar, Evelyn Heriot-Watt University
Ding, Jie University of Edinburgh
Ernst, Oliver TU Bergakademie Freiberg
Ferro, Maria Università di Napoli 'Federico II'
Gordon, Andrew University Of Manchester
Gyongy, Istvan University of Edinburgh
Hall, Eric University of Edinburgh
Hausenblas, Erika University Leoben
Jenny, Patrick ETH Zurich
Jentzen, Arnulf ETH Zurich
Kruse, Raphael University of Bielefeld
Krylov, Nicolai University of Minnesota
Kuske, Rachel University of British Columbia
Lakkis, Omar University of Sussex
Lord, Gabriel Heriot-Watt University
Lythe, Grant University of Leeds
Mugler, Antje University of Applied Science Zwickau
Nowak, Wolfgang University of Stuttgart
Riedler, Martin Heriot-Watt University
Scheichl, Rob University of Bath
Schmid, Karen University of Stuttgart
Sebastian, Geiger Heriot-Watt University
Shardlow, Tony
Sickenberger, Thorsten Heriot-Watt University
Stanciulescu, Vasile University of Leicester
Starkloff, Hans-Jörg University of Applied Sciences Zwickau
Yi, Liu AWE plc