@Article{NMTMA-15-3,
author = {R.M., Barron and M., Esmaeilzadeh and R.M., Barron},
title = {Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part II: Higher-Order Schemes},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2022},
volume = {15},
number = {3},
pages = {819--850},
abstract = {<p style="text-align: justify;">Compact higher-order (HO) schemes for a new finite difference method,
referred to as the Cartesian cut-stencil FD method, for the numerical solution of
the convection-diffusion equation in complex shaped domains have been addressed
in this paper. The Cartesian cut-stencil FD method, which employs 1-D quadratic
transformation functions to map a non-uniform (uncut or cut) physical stencil to
a uniform computational stencil, can be combined with compact HO Padé-Hermitian
formulations to produce HO cut-stencil schemes. The modified partial differential
equation technique is used to develop formulas for the local truncation error for the
cut-stencil HO formulations. The effect of various HO approximations for Neumann
boundary conditions on the solution accuracy and global order of convergence are
discussed. The numerical results for second-order and compact HO formulations of
the Cartesian cut-stencil FD method have been compared for test problems using the
method of manufactured solutions.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2021-0129},
url = {https://global-sci.com/article/90273/numerical-solution-of-partial-differential-equations-in-arbitrary-shaped-domains-using-cartesian-cut-stencil-finite-difference-method-part-ii-higher-order-schemes}
}