Numerical methods of elliptic equations with additive rough noise


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.