Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations

Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations

This is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A ...

Perturbing Fully Nonlinear Second Order Elliptic Equations

We present two types of perturbations with reverse effects on some scalar fully nonlinear second order elliptic differential operators: on the other hand, first order perturbations which destroy the global solvability of the Dirichlet problem, in smooth bounded domains of Rn; on the other hand, an integral perturbation which restore the local solvability, on compact connected manifolds without ...

Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow

Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out. In particular, it is found that ...

Higher Order Derivative Estimates for Finite-difference Schemes for Linear Elliptic and Parabolic Equations

Local Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations

This paper is concerned with developing accurate and efficient nonstandard discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary goal of the paper to develop a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity...