Numerical methods of elliptic equations with additive rough noise

Speaker:   Prof. Zhongqiang Zhang

Time:       10:00-11:00, July 9

Location:  SIST 1A 108

Host:       Prof. Qifeng Liao

Abstract:

We  consider finite  element  methods  for  a  class  of  semilinear  elliptic  equations  with  additive  spatial  noise. A key component of our numerical methods is spectral expansions for the spatial noise including white noise and fractional  white noise.  Taking a proper truncation of the  spectral  approximation,  we  prove  optimal  strong  convergence  order  of  the  finite  element approximation.  We also discuss the weak convergence of the considered numerical methods.  Numerical results confirm our prediction for one- and two-dimensional elliptic problems.

Bio:

Zhongqiang Zhang (张中强) is an Assistant Professor of Mathematics at Worcester Polytechnic Institute.  His research interests include numerical methods for stochastic and integral differential equations and their applications. Before he joined in Worcester Polytechnic Institute in 2014, he received Ph.D. degrees in mathematics at Shanghai University in 2011 and in applied mathematics at  Brown University in 2014.  He co-authored a book with George Karniadakis on numerical methods for stochastic partial differential equations.