This webpage collects information on the STINT Joint China-Sweden Mobility Numerical methods for stochastic partial differential equations CH2016-6729. This mobility program involves the following partners (with main participants in parentheses): Chinese Academy of Sciences (Jialin Hong, Zhou Tao), Central South University (Xiaojie Wang), Chalmers University of Technology and University of Gothenburg (Mihaly Kovacs, Annika Lang, Stig Larsson), and Umeå University (David Cohen).


Informal kick-off meeting at the Chinese Academy of Sciences, Beijing
May 27-28, 2017, Chinese Academy of Sciences, Beijing

In connection with the Forum on Scientific and Engineering Computing 2017.



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

This mini-course is given by Stig Larsson (Göteborg).
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:

  • Stochastic integration in Hilbert space. Stochastic evolution problem in Hilbert space. Semigroup, mild solution. Stochastic heat equation. Stochastic wave equation.
  • Numerical approximation by finite elements and Euler's method. Strong convergence.
  • Weak convergence. Malliavin calculus.
  • Stochastic Cahn--Hilliard equation.

    Sponsors

    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



    Scientific event on numerical methods for stochastic partial differential equations
    June 11-15, 2018, Chalmers University of Technology and the University of Gothenburg, Gothenburg

    We plan to organise a scientific meeting on numerical methods for stochastic (partial) differential equations connected, in some way, to the 40th Conference on Stochastic Processes and their Applications SPA 2018. Further information will follow.

    Contacts

    David Cohen

    Department of Mathematics and Mathematical Statistics
    Umeå universitet
    SE-90187 Umeå

    Annika Lang

    Department of Mathematical Sciences
    Chalmers University of Technology
    SE-412 96 Göteborg



    Last modifications: 20.11.17