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Journal of Scientific Computing

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24-10-2017

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

Authors: Brittany Froese Hamfeldt, Tiago Salvador

Published in: Journal of Scientific Computing | Issue 3/2018

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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.

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Title: Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations
Authors: Brittany Froese Hamfeldt
Tiago Salvador
Publication date: 24-10-2017
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0586-5

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