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Xiaobing Feng
Researcher at University of Tennessee
Publications - 124
Citations - 3641
Xiaobing Feng is an academic researcher from University of Tennessee. The author has contributed to research in topics: Finite element method & Numerical analysis. The author has an hindex of 28, co-authored 105 publications receiving 2917 citations. Previous affiliations of Xiaobing Feng include National University of Singapore & Shanghai Jiao Tong University.
Papers
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Journal ArticleDOI
Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
Xiaobing Feng,Andreas Prohl +1 more
TL;DR: Optimal order and quasi-optimal order error bounds are shown for the semi-discrete and fully discrete schemes under different constraints on the mesh size h and the time step size k and different regularity assumptions on the initial datum function u0.
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Fully Discrete Finite Element Approximations of the Navier--Stokes--Cahn-Hilliard Diffuse Interface Model for Two-Phase Fluid Flows
TL;DR: It is shown that the proposed numerical methods satisfy a mass conservation law, and a discrete energy law which is analogous to the basic energy law for the phase field model.
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Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
Xiaobing Feng,Haijun Wu +1 more
TL;DR: This paper develops and analyzes some interior penalty discontinuous Galerkin (IPDG) methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in two and three dimensions and proves that they are stable and well-posed.
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Error analysis of a mixed finite element method for the Cahn-Hilliard equation
Xiaobing Feng,Andreas Prohl +1 more
TL;DR: It is shown that all error bounds depend on only in some lower polynomial order for small ɛ, and convergence of the fully discrete finite element solution to the solution of the Hele-Shaw (Mullins-Sekerka) problem is proved.
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Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations
TL;DR: This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDEs) and intends to introduce these current advancements and new results to the SIAM community and generate more interest in numerical methods for fully non linear PDEs.