Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations. - Xiaobing Feng 001; Chiu-Yen Kao; Thomas L. Lewis (J. Comput. Appl. Math., 2013)

Local Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations. - Xiaobing Feng 001; Thomas L. Lewis (J. Sci. Comput., 2014)

Convergence Analysis of a Symmetric Dual-Wind Discontinuous Galerkin Method. - Thomas L. Lewis; Michael Neilan (J. Sci. Comput., 2014)

Discontinuous Galerkin finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations. - Xiaobing Feng 001; Thomas L. Lewis; Michael Neilan (J. Comput. Appl. Math., 2016)

Nonstandard Local Discontinuous Galerkin Methods for Fully Nonlinear Second Order Elliptic and Parabolic Equations in High Dimensions. - Xiaobing Feng 001; Thomas L. Lewis (J. Sci. Comput., 2018)

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 001; Thomas L. Lewis (CoRR, 2019)

A Narrow-stencil Finite Difference Method for Approximating Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. - Xiaobing Feng 001; Thomas L. Lewis (SIAM J. Numer. Anal., 2021)

A narrow-stencil framework for convergent numerical approximations of fully nonlinear second order PDEs. - Xiaobing Feng 001; Thomas L. Lewis; Kellie Ward (CoRR, 2022)

Convergence, stability analysis, and solvers for approximating sublinear positone and semipositone boundary value problems using finite difference methods. - Thomas L. Lewis; Quinn Morris; Yi Zhang (J. Comput. Appl. Math., 2022)

Convergence analysis of a symmetric dual-wind discontinuous Galerkin method for a parabolic variational inequality. - Satyajith Bommana Boyana; Thomas L. Lewis; Aaron Rapp; Yi Zhang (J. Comput. Appl. Math., 2023)

Consistency results for the dual-wind discontinuous Galerkin method. - Thomas L. Lewis; Aaron Rapp; Yi Zhang (J. Comput. Appl. Math., 2023)

Convergence analysis of novel discontinuous Galerkin methods for a convection dominated problem. - Satyajith Bommana Boyana; Thomas L. Lewis; Sijing Liu; Yi Zhang (CoRR, 2024)

Convergence Analysis of a Dual-Wind Discontinuous Galerkin Method for an Elliptic Optimal Control Problem with Control Constraints. - Satyajith Bommana Boyana; Thomas L. Lewis; Sijing Liu; Yi Zhang (CoRR, 2025)