109 citations · 289 across the 56 of their papers we have counts for
58 papers
An efficient and fast sparse grid algorithm for high-dimensional numerical integration
Huicong Zhong, Xiaobing Feng
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the -dimensional integral of a given fun…
A fast multilevel dimension iteration algorithm for high dimensional numerical integration
Xiaobing Feng, Huicong Zhong
In this paper, we propose and study a fast multilevel dimension iteration (MDI) algorithm for computing arbitrary -dimensional integrals based on tensor product approximations.…
High moment and pathwise error estimates for fully discrete mixed finite element approximattions of stochastic Navier-Stokes equations with additive noise
Xiaobing Feng, Liet Vo
This paper is concerned with high moment and pathwise error estimates for fully discrete mixed finite element approximattions of stochastic Navier-Stokes equations with general add…
Fully discrete finite element methods for nonlinear stochastic elastic wave equations with multiplicative noise
Xiaobing Feng, Yukun Li, Yujian Lin
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise.…
Higher order time discretization for the stochastic semilinear wave equation with multiplicative noise
Xiaobing Feng, Akash Ashirbad Panda, Andreas Prohl
In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicativ…
An efficient multi-modes Monte Carlo homogenization method for random materials
Zihao Yang, Jizu Huang, Xiaobing Feng +1
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homo…
A narrow-stencil framework for convergent numerical approximations of fully nonlinear second order PDEs
Xiaobing Feng, Thomas Lewis, Kellie Ward
This paper develops a unified general framework for designing convergent finite difference and discontinuous Galerkin methods for approximating viscosity and regular solutions of f…
On a New Class of Fractional Calculus of Variations and Related Fractional Differential Equations
Xiaobing Feng, Mitchell Sutton
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the exi…
An efficient iterative method for solving parameter-dependent and random convention-diffusion problems
Xiaobing Feng, Yan Luo, Liet Vo +1
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of…
Analysis of Chorin-Type Projection Methods for the Stochastic Stokes Equations with General Multiplicative Noises
Xiaobing Feng, Liet Vo
This paper is concerned with numerical analysis of two fully discrete Chorin-type projection methods for the stochastic Stokes equations with general non-solenoidal multiplicative…
On New Families of Fractional Sobolev Spaces
Xiaobing Feng, Mitchell Sutton
This paper presents three new families of fractional Sobolev spaces and their accompanying theory in one-dimension. The new construction and theory are based on a newly developed n…
A new theory of fractional differential calculus
Xiaobing Feng, Mitchell Sutton
This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional deri…
Optimally Convergent Mixed Finite Element Methods for the Stochastic Stokes Equations
Xiaobing Feng, Andreas Prohl, Liet Vo
We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving…
High-order mass- and energy-conserving SAV-Gauss collocation finite element methods for the nonlinear Schrödinger equation
Xiaobing Feng, Buyang Li, Shu Ma
A family of arbitrarily high-order fully discrete space-time finite element methods are proposed for the nonlinear Schrödinger equation based on the scalar auxiliary variable formu…
A new theory of fractional differential calculus and fractional Sobolev spaces: One-dimensional case
Xiaobing Feng, Mitchell Sutton
This paper presents a self-contained new theory of weak fractional differential calculus and fractional Sobolev spaces in one-dimension. The crux of this new theory is the introduc…
-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…
Strong convergence of a fully discrete finite element method for a class of semilinear stochastic partial differential equations with multiplicative noise
Xiaobing Feng, Yukun Li, Yi Zhang
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The n…
An efficient Monte Carlo interior penalty discontinuous Galerkin method for the time-harmonic Maxwell's equations with random coefficients
Xiaobing Feng, Junshan Lin, Cody Lorton
This paper develops an efficient Monte Carlo interior penalty discontinuous Galerkin method for electromagnetic wave propagation in random media. This method is based on a multi-mo…
A New Approach for 4DVar Data Assimilation
Xiangjun Tian, Aiguo Dai, Xiaobing Feng +3
Four-dimensional variational data assimilation (4DVar) has become an increasingly important tool in data science with wide applications in many engineering and scientific fields su…