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

Document Type

Article

Publication Date

6-1-2018

Abstract

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.

Identifier

85032029724 (Scopus)

Publication Title

Journal of Scientific Computing

External Full Text Location

https://doi.org/10.1007/s10915-017-0586-5

ISSN

08857474

First Page

1282

Last Page

1306

Issue

3

Volume

75

Grant

DMS-1619807

Fund Ref

National Science Foundation

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