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.
Scientific event on numerical methods for stochastic partial differential equations
June 11-15, 2018, Chalmers University of Technology and the University of Gothenburg, Gothenburg
Chalmers University of Technology
SE-412 96 Göteborg
David CohenDepartment of Mathematics and Mathematical Statistics
Annika LangDepartment of Mathematical Sciences