Rate My Professor Xiaobing Feng

Feng's research specializes in computational and applied mathematics, with a focus on numerical partial differential equations (PDEs) and scientific computing. His interests include high-dimensional computation, analysis and numerical methods for nonlinear PDEs, stochastic PDEs, fractional calculus, and nonlocal differential equations. He has developed finite element and discontinuous Galerkin methods for fully nonlinear second-order PDEs, data assimilation techniques such as 4DVar and i4DVar, phase field models for moving interfaces, and models for random media and wave scattering. Key publications include 'Optimal Order Space-Time Discretization Methods for the Nonlinear Stochastic Elastic Wave Equations With Multiplicative Noise' (2026), 'Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization' (2025), 'Higher order time discretization for the stochastic semilinear wave equation with multiplicative noise' (2023), 'Narrow-stencil framework for convergent numerical approximations of fully nonlinear second order PDEs' (2022), and 'Numerical analysis of the Allen-Cahn equation and approximation by finite differences' (2003). With over 161 publications and more than 5,500 citations, his work has significant impact in the field. In 2014, he received the Chancellor’s Award for Research and Creative Achievement, recognizing him as a world leader in numerical methods for fully nonlinear elliptic and parabolic PDEs. He has delivered invited lectures, including at Oak Ridge National Laboratory on reinventing computational mathematics for high-dimensional scientific computing.