109 citations · 289 across the 56 of their papers we have counts for
6 papers · 1 filter
-norm error estimate for a nonstandard finite element approximation of second-order linear elliptic PDEs in non-divergence form
Xiaobing Feng, Stefan Schnake
This paper establishes the optimal -norm error estimate for a nonstandard finite element method for approximating strong solutions of second order linear elliptic PDEs i…
A Narrow-stencil finite difference method for approximating viscosity solutions of fully nonlinear elliptic partial differential equations with applications to Hamilton-Jacobi-Bellman equations
Xiaobing Feng, Thomas Lewis
This paper presents a new narrow-stencil finite difference method for approximating the viscosity solution of second order fully nonlinear elliptic partial differential equations i…
Analysis of Fully Discrete Mixed Finite Element Methods for Time-dependent Stochastic Stokes Equations with Multiplicative Noise
Xiaobing Feng, Hailong Qiu
This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method,…
Fully Discrete Mixed Finite Element Methods for the Stochastic Cahn-Hilliard Equation with Gradient-type Multiplicative Noise
Xiaobing Feng, Yukun Li, Yi Zhang
This paper develops and analyzes some fully discrete mixed finite element methods for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise that is white in…
Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations
Xiaobing Feng, Hailiang Liu, Shu Ma
In this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schrödinger equations. The proposed schemes all satisfy both mass conservation and e…
The Phase Field Method for Geometric Moving Interfaces and Their Numerical Approximations
Qiang Du, Xiaobing Feng
This paper surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instea…