David Cohen Annika Lang
Visit of a Chinese delegation at Umeå University
October 31 - November 03, 2017, Umeå University, Umeå
Mini-course on Numerical methods for SPDE: strong and weak convergence analysis
November 06-10, 2017, Chinese Academy of Sciences, Beijing
The mini-course presents a survey of methods for proving strong convergence and weak convergence of numerical methods for the stochastic heat and wave equations. Strong convergence refers to convergence with respect to a norm, for example, mean square convergence. Proofs typically involve representation of the error using the semigroup theory or energy estimates and using the Ito isometry or the Burkhold--Davies--Gundy inequality. Weak convergence involves the error in some functional of the solution. Proofs may involve representation of the weak error in terms of the Kolmogorov equation and may use integration by parts from the Malliavin calculus. The main part of the lectures will be concerned with the linear stochastic heat and wave equations. As an example of a more difficult problem, we will briefly discuss the stochastic Cahn--Hilliard equation.
Topics covered in this mini-course are:
This mini-course is organised by Jialin Hong and David Cohen
within the framework Joint China-Sweden Mobility Grant of the Swedish Foundation for
International Cooperation in Research and Higher Education
STINT and the National Natural Science Foundation of China
NSFC. We gratefully acknowledge its financial support.
We thank the Institute of Computational Mathematics at the Chinese Academy of Sciences (CAS) for the hospitality.
Further information can be found here.
And finally a picture from the classroom:
Visit of a Swedish delegation at Shandong University (Jinan), Central South University (Changsha) and Hunan Normal (Changsha)
November 13 - November 17, 2017
Visit of a Swedish delegation at CAS (Beijing) and Central South University (Changsha)
May 13 - June 03, 2018
Scientific event on numerical methods for stochastic partial differential equations
June 11-15, 2018, Chalmers University of Technology and the University of Gothenburg, Gothenburg
Visit of a Swedish delegation at CAS (Beijing) and forum on numerical analysis of SPDE
October 10 - October 19, 2018
And the traditional group photo:
March 09, 2019
Workshop Numerical Methods for SPDE: 20 successful years and future challenges at the Mittag-Leffler Institute
May 20-24, 2019
July 07, 2019
Visit of a Swedish delegation at CAS (Beijing), Qufu Normal University (Qufu), Nanchang University (Nanchang),
and Central South University (Changsha)
September 9 - September 25, 2019
Visit of a Chinese delegation at Chalmers University of Technology (Göteborg)
November 3 - November 9, 2019
Online crash course on numerics for SDEs at Central South University (Changsha)
The mini-course is designed to give a concise and accessible introduction to numerical discretisations of stochastic differential equations (SDEs). We assume only a basic competence in calculus and probability theory. Topics: Basics of stochastic processes and SDEs. Numerical methods for SDEs. Strong and weak convergence. Applications.
The introductory slides.
Some figures and photos from the lecture.
Some computer labs.
A scan of my lecture notes.
Time for the online lectures (a zoom link is provided by Xiaojie Wang):
Tuesday 15 September 2020: 9:00 AM to ca. 11:00 AM, Gothenburg time (15:00-17:00 Beijing time)
Friday 18 September 2020: 9:00 AM to ca. 11:00 AM, Gothenburg time (15:00-17:00 Beijing time)
Tuesday 22 September 2020: 9:00 AM to ca. 11:00 AM, Gothenburg time (15:00-17:00 Beijing time)
Thursday 24 September 2020: 9:00 AM to ca. 11:00 AM, Gothenburg time (15:00-17:00 Beijing time)
We gratefully acknowledge the additional financial support of the School of Mathematics and Statistics at Central South University.
Chalmers University of Technology
SE-412 96 Göteborg and Department of Mathematics and Mathematical Statistics
Chalmers University of Technology
SE-412 96 Göteborg
David CohenDepartment of Mathematical Sciences
Annika LangDepartment of Mathematical Sciences