21 citations · 30 across the 8 of their papers we have counts for
8 papers
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…
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…
Nonstandard local discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic equations in high dimensions
Xiaobing Feng, Thomas Lewis
This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in mu…
Analysis of the Vanishing Moment Method and its Finite Element Approximations for Second-order Linear Elliptic PDEs in Non-divergence Form
Xiaobing Feng, Thomas Lewis, Stefan Schnake
This paper is concerned with continuous and discrete approximations of strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-diver…
Discontinuous Galerkin finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations
Xiaobing Feng, Thomas Lewis, Michael Neilan
This paper develops a discontinuous Galerkin (DG) finite element differential calculus theory for approximating weak derivatives of Sobolev functions and piecewise Sobolev function…
Local discontinuous Galerkin methods for one-dimensional second order fully nonlinear elliptic and parabolic equations
Xiaobing Feng, Thomas Lewis
This paper is concerned with developing accurate and efficient discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations…
Mixed Interior Penalty Discontinuous Galerkin Methods for One-dimensional Fully Nonlinear Second Order Elliptic and Parabolic Equations
Xiaobing Feng, Thomas Lewis
This paper is concerned with developing accurate and efficient numerical methods for one-dimensional fully nonlinear second order elliptic and parabolic partial differential equati…
Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations
Xiaobing Feng, Chiu-Yen Kao, Thomas Lewis
This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully…