Work

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

Year: 2017

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1706.07741

Authors: Froese, Brittany D., Salvador, Tiago

Language: English

Topic: Numerical methods in engineering

Subfield: Mechanics of Materials

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Natural Sciences and Engineering Research Council of Canada

Awards: Numerical Methods for Nonlinear Partial Differential Equations, with applications to Optimal Transportation, and Geometric Data Reduction, Meshfree Finite Difference Methods for Nonlinear Elliptic Equations

OpenAlex ID: W2962872171

Cites: 18

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Related to: 20