主講人：Professor Zhang Zhongqiang,Worcester Polytechnic Institute
主講人介紹：Zhongqiang Zhang is 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.
內容介紹：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.