Numerical methods of elliptic equations with additive rough noise


主讲人:Professor Zhang Zhongqiang,Worcester Polytechnic Institute




主讲人介绍: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.

内容介绍: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.