報告題目： An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise
報告人：Professor Yubin Yan（University of Chester, UK）
報告地點：騰訊會議 957 252 674
報告摘要： We consider the strong convergence of the numerical methods for solving stochastic subdiffusion problem driven by an integrated space-time white noise. The time fractional derivative is approximated by using the L1 scheme and the time fractional integral is approximated with the Lubich's first order convolution quadrature formula. We use the Euler method to approximate the noise in time and use the truncated series to approximate the noise in space. The spatial variable is discretized by using the linear finite element method. Applying the idea in Gunzburger \et (Math. Comp. 88(2019), pp. 1715-1741), we express the approximate solutions of the fully discrete scheme by the convolution of the piecewise constant function and the inverse Laplace transform of the resolvent related function. Based on such convolution expressions of the approximate solutions, we obtain the optimal convergence orders of the fully discrete scheme in spatial multi-dimensional cases by using the Laplace transform method and the corresponding resolvent estimates.
報告人簡介：Dr Yubin Yan, born in April 8th, 1965, works in the Department of Mathematical and Physical Sciences at University of Chester, UK. He obtained his PhD degree in Mathematics in Chalmers University of Technology in 2003 and was the research associate in University of Manchester (2003-2004) and University of Chester (2004-2007). His research area is numerical analysis for the stochastic and deterministic (partial) differential equation, finite element method, and numerical method for fractional differential equation. He introduced a new framework in 2005 for the error estimates of the finite element method for stochastic parabolic equation which is now regarded as the standard reference in this research area. Up to now he published more than 60 refereed papers on SIAM J. Numerical Analysis, BIT, IMA J. Numerical Analysis, etc. He supervised 3 PhD theses and 20 MSc dissertations. Currently he is supervising 3 PhD students. He is the regular referee for more than 30 scientific journals. He is now in the Editorial boards of several international research journals including Applied Numerical Mathematics, Frontier of Physics, etc. His citation number is 924 and h-index is 15 in Google Scholar.