TY - JOUR
T1 - Analysis of Hexagonal Grid Finite Difference Methods for Anisotropic Laplacian Related Equations
AU - Daniel Lee
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 562
EP - 596
PY - 2017
DA - 2017/10
SN - 10
DO - http://doi.org/10.4208/nmtma.2017.m1527
UR - https://global-sci.org/intro/article_detail/nmtma/12359.html
KW - 
AB - <p style="text-align: justify;">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.</p>