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

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated geometries, while still ensuring...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-06
Main Authors: Froese, Brittany D, Salvador, Tiago
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Elliptic functions
Finite difference method
Mathematical analysis
Nonlinear equations
Partial differential equations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated geometries, while still ensuring consistency, monotonicity, and convergence. We describe an algorithm for efficiently computing the non-traditional finite difference stencils. We also present a strategy for computing formally higher-order convergent methods. Computational examples demonstrate the efficiency, accuracy, and flexibility of the methods.
ISSN:2331-8422