Analysis of Hexagonal Grid Finite Difference Methods for Anisotropic Laplacian Related Equations

Analysis of Hexagonal Grid Finite Difference Methods for Anisotropic Laplacian Related Equations

Year:    2017

Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 562–596

Abstract

Hexagonal grids are valuable in two-dimensional applications involving Laplacian. The methods and analysis are investigated in current work in both linear and nonlinear problems related to anisotropic Laplacian. Ordinary and compact hexagonal grid finite difference methods are developed by elementary arguments, and then analyzed by perturbation for standard Laplacian. In the anisotropic case, analysis is done through reduction to the standard one by using Fourier vectors of mixed types. These hexagonal seven-point methods, with established theoretic stabilities and accuracies, are numerically confirmed in linear and semi-linear anisotropic Poisson problems, and can also be applied in time-dependent problems and in many applications in two-dimensional irregular domains.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2017.m1527

Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 3 : pp. 562–596

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords: